For me personally these are the best zoological facilities from the states where I've visited ones in. I know OP didn't include aquariums but I think they should be and I don't think a new thread is necessary just to include them so I will be adding them in my list. I'm also including number of zoos I visited in each state in parentheses, this can include true zoos, aquariums, safari parks, specialist collections and nature centers/museums with at least some wild mammals/birds of prey.
Alabama (9): Montgomery Zoo
Montgomery Zoo beats out the AZA-accredited Birmingham Zoo thanks to great savanna exhibits and more consistent quality. The Mann Museum is also really cool and has a great North American taxidermy collection. Although Birmingham has a more diverse collection of birds and small carnivores, there are too many really subpar exhibits that bring it down. I've visited probably the majority of zoological facilities in Alabama and besides the big two there is a surprising number of small but solid facilities here.
Arizona (4): Phoenix Zoo
Phoenix Zoo is overall a very good traditional zoo, with a wonderful Arizona-themed complex. Odysea Aquarium, Out Of Africa (surprisingly good for non-AZA) and Goldfield Mines Serpentarium are the other facilities I visited in the state. I have not visited ASDM or Wildlife World, but the formers animal collection has declined greatly and its exclusively/largely a native-only zoo while the latter has some really poor quality areas so I don't think either would knock Phoenix off the top spot but I can't say for certain until I visit.
California (3): San Diego Zoo
I prefer the larger and more diverse collection at SDZ over the safari park. I've only visited those two and Los Angeles, but pretty confident San Diego would win even if I visited every collection in the state.
Connecticut (7): Mystic Aquarium
I prefer both of the states main aquariums over Beardsley Zoo, but its Mystics excellent marine mammal collection and Beluga exhibit that seals (no pun intended) the deal. I suspect Beardsley would win by default if aquariums are excluded simply because there really isn't really any other traditional zoo in the state.
Delaware (1): Brandywine Zoo
A tiny and forgettable zoo but it wins by default since there isn't much else.
Florida (~70): Zoo Miami
I've visited pretty much all the major zoos in the state and many of the smaller places, and Miami still ranks as the best for me. Its sad to see the rarities slowly dying out but I love the tropical naturalistic design of the zoo and its exhibit complexes. I prefer traditional zoos like Miami and Jacksonville (runner-up) over the theme park zoos like DAK and Busch Gardens, which are both very good as well but don't have as large of a collection and have all the negative associations expected of major theme parks like insane lines and crowds, limited access to special exhibits and high prices.
Georgia (20): Georgia Aquarium
Whale Sharks, mantas, Tiger Sharks, Ocean Voyager. This aquarium is phenomenal and even as someone who prefers traditional zoos to aquariums, there's no way Zoo Atlanta can beat the unique and amazing experience at Georgia Aquarium. Atlanta is a very good zoo that I feel punches above its weight and would easily be best in state if I had to exclude the aquarium, but admittedly there isn't any real competition as most of the other zoos in Georgia are either good but small nature center-type places or junky roadsides and meh safari parks.
Louisiana (7): Audubon Zoo
I took a zoo trip to Louisiana this summer and while I didn't revisit Audubon Zoo this trip I can safely say it beats out all the other traditional zoos in the state, although Alexandria and Baton Rouge each have some charm. I've never been to the Audubon Aquarium but I doubt I'd take it over the zoo especially with no marine mammals present outside of Sea Otters.
Maryland (7 + National Zoo): National Aquarium (or National Zoo)
Keeping this strictly to Maryland, I would go with National Aquarium, although if I'm being honest compared to most others who have visited I was slightly disappointed with it. Its probably due to the odd layout of the facility and Australia being a lot smaller than I thought it would be as well as the fact that I generally prefer traditional zoos over aquariums. Still, the quality is great and I did love the Rainforest area. My runner up and non-aquarium pick would be Maryland Zoo and was thinking of giving it the upset but until they rebuild the abandoned entrance area and improve the primate exhibits I'm choosing the aquarium. If I lumped DC into Maryland, National Zoo would easily be my pick as favorite.
Massachusetts (2): Franklin Park Zoo
If you judge it as the zoological representation of Boston, FPZ could be considered one of the most disappointing zoos in America. But on its own its a decent facility and I would take it over Stone Zoo. Those are the only 2 zoos I visited in the state and since both aren't very large and have their flaws its possible Southwicks, Buttonwood Park or NE Aquarium could win if I ever get to them.
Mississippi (5): Mississippi Aquarium
A very enjoyable aquarium that few zoochatters will ever visit due to being located in Mississippi. Hattiesburg Zoo would be my choice if no aquariums are allowed but its not even that good of a zoo, it just beats out the rest of the hellholes in the state like Tupelo Buffalo Park and Jackson Zoo (I only visited the first one).
Nevada (1): Shark Reef Aquarium
This is the only facility I visited but there really is nothing else to compete with it, Nevada is a zoological wasteland. Animal Ark would be the closest thing to a non-aquarium zoo in the state. Its a crime Las Vegas doesn't have a traditional accredited zoo.
New Jersey (12): Cape May Zoo
Free admission and preferring zoos over aquariums is a big advantage for Cape May here. I also really enjoyed the reptile house. Adventure Aquarium was a very close second though and Turtle Back Zoo is close behind as well. Maybe Six Flags Safari could win if I ever visit?
New York (21): Bronx Zoo
I haven't visited Buffalo Zoo and a handful of tiny places but I can say with 100% confidence Bronx is the best zoo in the state (not a bold statement either).
North Carolina (11): North Carolina Zoo
NC Zoo has one of the highest levels of exhibit quality I've ever seen, although the limited collection prevents it from reaching its true potential (that could change soon with Asia and other expansions). I really enjoyed Greensboro as well and consider it a worthy competitor. I haven't visited any of the aquariums or the really interesting Sylvan Heights Bird Park.
Ohio (7): Columbus Zoo & Aquarium
I visited Ohio in the spring and managed to visit Columbus, Cleveland, Akron and the Wilds as well as a number of nature centers in the Cleveland Metro area (of which I personally only count 3 as large enough to qualify as zoological facilities). All these zoos were good to great, but Columbus truly lived up to its reputation as one of the best zoos in the country although it lacks the collection size to compete with places like Bronx and San Diego (and Omaha most likely as well). I didn't get to visit Toledo or Cincinnati so perhaps either of those two could offer competition.
Pennsylvania (12): Pittsburgh Zoo & Aquarium
It was a tough choice between Pittsburgh and Philadelphia, but as of now I'm inclined to give Pittsburgh the edge. I think the highs and lows at Pitt are more extreme than Philadelphia, but its those positive highs that make it stand out more. The aquarium building at Pittsburgh is also very well done for an "inside-zoo" aquarium. Philadelphia has a better collection in my opinion and some exhibit highlights like zoo360 and the bird house, but the collection has been on the decline and a lot of areas are really of very average to below average quality. Plus I have no idea what the heck they were going for with the Water is Life complex.
Rhode Island (2): Roger Williams Park Zoo
Save The Bay Aquarium was a nice amateurish aquarium center but there's no way it could compete with what might be the best traditional zoo in New England (though thats not saying much). Nothing else in the tiny state will come close to matching RWPZ I can guarantee.
South Carolina (6): Riverbanks Zoo
Riverbanks is a pretty solid although clearly outdated in areas. I did sadly miss the opening of the new ARC. I don't think there is really any competition within the state, unless South Carolina Aquarium is much better than I think it would be.
Tennessee (9): Memphis Zoo
I had to visit Tennessee several times this year and I did get the pleasure to tour all the major zoos and aquariums in the state. Although tempted to give the excellent Tennessee Aquarium the nod for the best in state, I have to take the traditional approach and go with the also excellent Memphis Zoo. Although the elephant exhibit isn't very good, I think its an underrated zoo overall and I personally rank it as one of my favorite zoo experiences. I will say that once Nashville Zoo completes its planned African expansion it may very well become best in the state, the quality of all their new completed projects have been excellent.
Virginia (1): Virginia Zoo
I thought Virginia Zoo was a pretty good place with a very comprehensive reptile house. I haven't visited any other zoos in the state, although the larger Metro Richmond Zoo seems to be of lower quality and the Virginia Aquarium doesn't seem to stand out much.
West Virginia (1): Oglebay Good Zoo
I got to visit this little zoo on the way back from my Ohio trip and I thought it was quite the nice facility. Definitely "good"

. I don't think any of the few other facilities in the state would be of much competition.
If I had to guess the best for the remaining states without having experienced any zoos within them.....
Alaska: Alaska Zoo
Arkansas: Little Rock Zoo
Colorado: Denver Zoo
Hawaii: Honolulu Zoo
Idaho: Zoo Boise
Illinois: Brookfield Zoo? Maybe Shedd.
Indiana: Indianapolis Zoo
Iowa: Blank Park Zoo
Kansas: Sedgwick County Zoo
Kentucky: Louisville Zoo
Maine: York's Wild Kingdom? Maybe Maine Wildlife Park.
Michigan: Detroit Zoo
Minnesota: Minnesota Zoo
Missouri: St. Louis Zoo
Montana: Zoo Montana
Nebraska: Omaha Zoo
New Hampshire: Squam Lakes Nature Center
New Mexico: ABQ Biopark Zoo
North Dakota: Dakota Zoo?
Oklahoma: Oklahoma City Zoo
Oregon: Oregon Zoo
South Dakota: Great Plains Zoo
Texas: Dallas Zoo or Houston Zoo or Fort Worth Zoo? Lots of choices.
Utah: Hogle Zoo? Maybe Tracy Aviary.
Vermont: VINS? Not much choices.
Washington: Woodland Park Zoo
Wisconsin: Milwaukee County Zoo? Maybe Henry Vilas.
Wyoming: Buffalo Bill Center? Not much choices.