Here are some other cities in the US I think could use a zoo besides my hometown Youngstown. Most of, if not all of these cities did once have a zoo but shut them down.
Rockford, Illinois
Hartford, Connecticut
Lima, Ohio
Iowa City, Iowa
Davenport, Iowa
Grand Forks, North Dakota
Ithaca, New York
Cheyenne, Wyoming
New Haven, Connecticut
Kingsport, Tennessee
Champaign, Illinois
Missoula, Montana
Lexington, Kentucky
Yuma, Arizona
Scranton, Pennsylvania (They have an Aquarium, Though)
Ogden, Utah
Lancaster, Pennsylvania
Augusta, Maine
Canton, Ohio
Queensbury, New York
Gatlinburg, Tennessee (They have a Ripley's Aquarium location though)
Casper, Wyoming
Concord, New Hampshire
Twin Falls, Idaho
Albany, New York
Charlotte, North Carolina
Raleigh, North Carolina
Winston-Salem, North Carolina
Bowling Green, Kentucky
Lawton, Oklahoma
Dubuque, Iowa (They have the National Mississippi River Museum and Aquarium though)
Anywhere in Vermont
I know, it's a lot of cities in need of a zoo.
I think a lot of these places are places that definitely could support a small AZA size zoo, such as the ones in middle of IL (Peoria, Miller Park, Scovill), but I don't think any of them could support a zoo of the size you are thinking. I also don't know if the majority truly "need" a zoo as most have at least one AZA collection of a significant size within pretty easy driving distance and aren't major cities that I would typically say should each have their own zoo. Driving an hour or so is not that crazy to most Americans and something within 2 hours or under is an easy day trip for most.
That all being said, lets take a closer look at each of the places you suggested:
Rockford, IL - Sort of agree they should have a small zoo of their own in the vein of Peoria, Miller Park in Bloomington, Scovill in Decatur, or Henson Robinson in Springfield, but there are a significant number of places within an easy day trip. Henry Vilas in Madison is just over an hour, Brookfield at an hour and a half, Lincoln Park just over that, Shedd at an hour and 40 minutes, and Milwaukee County at an 1.5 hours. Thats 5 establishments in America's Top 100 (according to Snowleopard's book) within under 2 hours. Additionally, the Summerfield Zoo is in the "suburbs" of Rockford and while small (and I can't vouch for its quality) it holds a surprising number of rarities. This ignores all the smaller places in an around Chicago that are also accessible in under 2 hours.
Hartford, CT - I'm not sure why, but being from the NYC, I agree Hartford feels quite isolated from a zoo. Perhaps this is because New England/East Coast feels quite compact compared to the rest of the US, so any sort of distance feels more significant. That being said, Beardsley and Mystic Aquarium (both AZA) are under an hour from Hartford, the Zoo in Forest Park and Lupa Zoo near Sprinfield are both 40 minutes or under, and Roger Williams (AZA) and Southwicks are both 1.5 hours or under. This doesn't even mention the 3 AZA facilities in Boston or the Bronx Zoo and others in NYC that are also all under 2 hours and again leaves out smaller places.
Lima, OH - Definitely a city that is sort of stuck in the middle of a lot of significant zoos without much in between. That being said, there are 3 significant AZA zoos under an hour and half from here in Fort Wayne, Toledo, and Columbus with Boonshoft in Dayton making 4 total. Additionally, Cincy is just under 2 hours and even more places open up if with go slightly over the 2 hour mark.
Iowa City/Dubuque (and Davenport could be lumped in), IA - Being from MN originally and going to school in La Crosse, WI this area was never far away from me and another I've always thought should have it's own zoo as well. Personally, I would put it in Cedar Rapids instead for several reasons, including (1) the closest zoo to this area is Niabi (fromerly AZA) in the Quad Cities area, which is only an hour from Iowa City, so Cedar Rapids gives the two a bit more space to call their own; (2) I think any zoo past something that is privately owned in this area is going to need to rely on the population of the entire area (Waterloo, Cedar Rapids, Iowa City and even Dubuque) and Cedar Rapids makes it a bit more centrally located and easier to access for Waterloo and Dubuque residents. Otherwise, I agree this area is pretty scarce in terms of collections. The Aquarium in Dubuque is within about a hour and half or less from most these people in addition to Niabi, but Blank Park is right at 2 hours for Iowa City and then everything else is a hike.
Davenport, IA - The first one that personally makes zero sense to me on this list. Niabi (formerly AZA, granted they lost this 10+ years ago, but largely due to budget concerns) is right across the border in IL and also in the Quad Cities metro area. I think you are putting to much emphasis on "it doesn't have a zoo in the city proper" so it needs one, while ignoring what is around it.
Grand Forks, ND - Red River is only a bit over an hour away, but with how small that AZA zoo is, Grand Forks could definitely use one of its own. Chahinkapa is about 2 hours, but with no major or mid-size zoo to access easily, this might be the a top contender for top city that needs a zoo based on the list you provided. That being said, it think whatever Grand Forks would support would end up being far smaller than what you have in mind. Additionally, western ND and the eastern half of Montana (along with NW South Dakota) are quite barren in terms of zoos and could use something, but I don't know if any town in this region could support much. Dickinson or Williston, ND would likely be the best bet, but I doubt either would support any sort of AZA type zoo and instead you would be looking at a smaller, city run place.
Ithaca, NY - Definitely a place that looks quite isolated zoo wise when looking at it on a map. Ithaca is quite a small city though to support a zoo and largely a college town, so I think they would have quite a bit of difficulty supporting any sort of significant zoo. Additionally, Rosamond Gifford in Syracuse is just over an hour away, along with Ross Park in Binghampton (formerly AZA). Seneca Park in Rochester and Utica are also AZA and right around 2 hours. Again, fairly easy access to zoos. There is also Animal Adventure not to far outside Binghampton.
Wyoming - Just taking these two cities together. I think Wyoming as a whole needs a zoo somewhere in the state (I'm aware there is a raptor center), I personally would put it in Casper as that gives it more separation from Denver and opens up access to more Wyoming residents. That being said, over 15% of the states population lives in Laramie County and would still be closer to Denver than a zoo in Casper. In terms of nearby collections for the state, you have the Riverside Discovery Center in Scottsbluff, NE (former AZA) and Reptile Gardens & Bear Country USA near Rapid City, SD that are within driving distance for residents based on where they live.
Concord, NH - Again, it probably needs more than it has, but it is within an easy drive of Boston and its three facilities their. Stone is under an hour and Squam Lakes in NH is under 45 minutes. While, Squam focuses on native animals only, it is quite a good little zoo. Best bet would for Manchester and Concord to team up if they truly wanted a zoo, but I don't think it is seen as a necessity here.
New Haven, CT - Another one that I don't quite understand or think they need a zoo at all. Beardsley is right there in Bridgeport. The two aquariums in the state are under and hour. Bronx is just over an hour. Yes, traffic lengthens these times, but lots of options very easily accessible.
Kingsport, TN - Another one I would have to disagree with personally. Brights Zoo is not far away and has a fairly significant collection for this area already and Zoo Knoxville can be reached within an hour and half. Additionally, the Briarwood Ranch Safari Park is not far. Are there other cities of a similar size that support there own zoos? Sure, but history plays a large role in many of these. In terms of the modern day realities, I definitely don't think Kingsport needs its own zoo.
Champaign, IL - I've sort of always though Urbana-Champaign should have its own zoo as well, but that is honestly largely due to the "city competition" side of things as I find it a bit strange from a historical stand point that all the other smaller cities in Champaign's part of the state have zoos (Peoria, Bloomington, Decatur, Springfield) and they don't. Reality is, Miller Park in Bloomington and Scovill are both under an hour and larger collections in Chicago and Indianapolis can be reached in about 2 hours. They aren't far from a zoo if they want to access one.
Missoula, MT - Likely another top contender here. I have something on my map called "Zootown Exotics" (which Google lists as permanently closed) that looks to be a rescue organization that publicly displays animals, but otherwise there is nothing here and not much within an easy drive.
Lexington, KY - In terms of size, this is definitely a top contender for city that needs a zoo on the list. That being said, Louisville and Cincy are not far, with smaller places (like Ark Encounter & Kentucky Reptile) being even closer.
Yuma, AZ - Definitely nothing around it in terms of zoological facilities and is a city of a decent size. Phoenix, Living Desert, and San Diego are all close to 3 hours away.
Scranton, PA - A fairly decent sized metro area not to have its own zoo. However, Claws-n-Paws Wild Animal Park is nearby though. In terms of AZA places, Lehigh Valley & Clyde Peeling's Reptiland are each about an hour and a half. Philly and the Bronx are around 2 hours, so definitely are options near by.
Ogden, UT - Another one that I have to go ask the question, does it really? Ogden is part of the Salt Lake City metro area, which already has the Hogle Zoo, Tracy Aviary, and Loveland Aquarium in terms of AZA places. There is also the former SeaQuest facility now operating as Layton Aquarium & Wildlife. And Zootah in Logan is under an hour away.
Lancaster, PA - Going to disagree on this one as well. ZooAmerica is within 30 minutes, with Philly, Maryland, National Aquarium, Adventure Aquarium, and Brandywine all under an hour and a half. Easy access to many options and is a smaller city like a lot of these that would not support anything that is significant.
Maine - Maine likely could do with a few better facilities than it has now, but the problem is the population is quite spread out making it hard to have a large enough concentration of people to support a place. I would argue Bangor is in more need of one than Augusta. Augusta at least has a few options close in terms of non-AZA places, while Bangor really doesn't.
Canton, OH - I really see this as the same argument I made for Youngstown. It is close enough to Akron and Cleveland for it to not need a zoo. I guess at least Canton has more of a tourist scene because of the Football Hall of Fame, which may help support a zoo, but I still don't really think it is necessary.
Queensbury, NY - Probably too small to support any sort of zoo. There are a few non-AZA places nearby for residents.
Gatlinburg/Pigeon Forge, TN - Largely a tourist town and zoos aren't typically a big draw for tourists. Zoos in similar places (Wisconsin Dells, Las Vegas, Branson, etc) are typically pretty junky and struggle as serious zoological institutions and have to rely on selling "interactions". Additionally, there are definitely zoological facilities in this area as I have been to 6 of them. In addition to the Aquarium, I have been to Ober Mountain Wildlife Habitat, Three Bears General Store, Parrot Mountain & Gardens, Rainforest Adventure Discovery Zoo, and Smoky Mountains Deer Farm & Exotic Petting Zoo.
Twin Falls, ID - Could probably support another small zoo in the vein of those also in Idaho (Idaho Falls & Zoo Idaho) as there really isn't anything else around. Zoo Boise and Zoo Idaho are both about 2 hours away.
Albany, NY - One the is mentioned fairly often on this site. There is an aquarium not farm and some smaller places, but could probably use its own zoo as well.
Charlotte, NC - Another one of the most commonly talked about ones and I would definitely agree. Unfortunately, I think any shot of a significant zoo in Charlotte went away when the state decided to open the North Carolina Zoo in between all the major metro areas of the state, which is only an 1.5 hours away. Charlotte also has the SEA LIFE facility that is apart of the AZA and Discovery Place has two sites with animals in the city (from what I can tell).
Raleigh, NC - Maybe, but probably not is my answer here. Part of the Raleigh-Durham metro, which has an AZA accredited zoo in the Museum of Life & Science which is more of a zoo than most realize. The Greensboro Science Center also isn't far, nor is the North Carolina Zoo.
Winston-Salem, NC - Again, part of a metro area with an AZA zoo (Greensboro Science Center) and not far from the North Carolina Zoo.
Bowling Green, KY - Again, maybe, but probably not. It may be isolated enough it needs its own zoo, but Nashville is only about an hour away and both Louisville and Mesker Park in Evansville, IN are about a hour and 45 minutes. Kentucky Down Under is even closer than the others.
Lawton, OK - Another maybe for me. Likely wouldn't be anything huge. Oklahoma City is only 1.5 hours away.
Vermont - I think Burlington/Montpelier could definitely use a zoo of its own. Whether it could support it, who knows.
Also, about Austin, just put it simply, modify the existing Austin Zoo, improve some of it's existing exhibits, and it's a proper zoo that is gonna get accredited once those changes are made.
I think this would be a lot harder than you think. AZA goes far beyond exhibitry and animal welfare in its accrediting process. I think the Austin Zoo is a long way off, personally. That being said, not every place or city needs to have an AZA zoo and I think you are placing too much emphasis on the AZA accredited part. Many places have solid zoos that are an asset to their communities that are not AZA accredited. Many zoos choose not seek AZA accreditation because doing so comes with having to spend more money on things that aren't directly related to running the zoo. While those things are definitely a good thing to support for zoos, not all can make it work budgetarily.