One facility I personally enjoy is Powder Valley. It has a nature center which features mostly native herps and fish, though I doubt any could be considered rare by any means. I have not been in a while, so I could not tell you off-hand what's in there now. Like many animal facilities, it is definitely kid-oriented, but there is a lot of good information on signage and some fun immersive elements. There's certainly a focus on education. It is also a great place to view naturally occurring wildlife. There is a viewing blind by a feeder area that is a great place for observation. Another facility is Grant's Farm. I documented it as of last year (photos are in the gallery), although each new season brings about new changes. I have not gotten the chance to visit this season yet but I will try to make it out there to document the changes for the 2023 season. My thoughts as of my last visit though is that it is definitely a charming little place. Not a rarity to be found and its largely domestics so do not visit for the collection but if you want to spend a fun day around animals you will probably enjoy your visit. How it works is visitors arrive and board trams which go through several different areas, one being the "Deer Park" which features free-roaming hoofstock and also passes by enclosures for animals like plains zebras and common ostriches. You are then dropped off into the Tier Garden, which features the various animal exhibits and is more like a typical zoo. The exhibit I was personally the most impressed with was the one for the ring-tailed lemurs. It is literally just an island with a modified swingset on it but it totally works. The swingset offers many climbing opportunities and allows visitors to see their impressive agility. As long as you manage your expectations, if its anything like it was last year, you'll probably have a good time. Its definitely family-oriented though so going just by myself as an young adult was a bit awkward. Neither of these facilities are worthy of making a trip to the city for, but they are worth checking out if you're in the area for the Saint Louis Zoo and/or World Bird Sanctuary and have some extra time on your hands.
I will also add that a lot of people (if not most) who go to the World Bird Sanctuary also do Lone Elk Park, which is right next to it. There are some photos in the gallery for your reference. As the name implies, part of the park does feature a drive through with elk, as well as American bison. The rest is a pretty standard nature park with a lake that is a good place for viewing naturally occurring wildlife.
Also Kansas City Zoo is not too far away if you ever get several consecutive days off.