I went birding/wildlife watching at the Wichita Mountains Wildlife Refuge a few years ago when I was in Oklahoma; it has a bison herd and is a pretty good birding spot as well. If you like art museums, the Philbrook in Tulsa is well-regarded and a nice place to spend a couple hours.
Oklahoma City Zoo: with the African exhibit not being open yet, you may not need a whole day for the zoo - maybe 4 to 5 hours. My best advice is try to be in the Reptile House whenever it is least crowded; it is difficult to walk in those hallways with even mild crowds. The rest of the zoo is much more spread out and roomy so should be fine.
Tulsa Zoo is a bit smaller but has a lot of smaller species and buildings, so I'd budget 3 to 4 hours for that one. They have a great collection of less frequently seen species spread throughout the zoo, but if you're into birds definitely check out the Conservation Center in particular.
Both lists are from 2021:
Species List for Oklahoma City Zoo:
Oklahoma City Zoo Species List - Nov 2021 [Oklahoma City Zoo]
Species List for Tulsa Zoo:
Tulsa Zoo Species List - Dec 2021 [Tulsa Zoo]
If you're looking for other places to visit, the Oklahoma Aquarium just outside Tulsa has the country's only Bull Sharks; you could probably fit that and the zoo into one day pretty easily.