Apparently Evansville, Indiana has a pretty nice little zoo. It's about ten acres smaller than Indianapolis's own (relatively modest) zoo, and houses 200 species to Indy's 320, but it's actually older, having been founded in 1928, well before Indianapolis's post-WWII zoo.
The only downside to visiting is that I'd probably want to overnight there. Evansville is the state's third most populous city, located down in the toe of the state. (The "toe" being in the southwest corner near the confluence of the Wabash and Ohio rivers.) Until I-69 gets completed, it's sort of in "you can't get there from here" territory for day trips from Indianapolis.
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