It depends on what you are looking for really. The Indiana Repertory Theatre is the local regional theatre. They tend to do safer plays. There is also the Phoenix (my favorite - though I am totally biased). They do much riskier material. They haven't announced their new season yet (and probably won't for a month or so), but it should be good. They are the ones doing the first regional production of Hand to God this summer. Then there is also Footlight Muscials, Theatre on the Square, and a few other smaller theatre companies throughout the area. You may also want to check out The Cabaret at the Columbia Club. We do have a "Broadway Across America" division here in Indy as well.
Bloomington (Indiana University) isn't too far away and has a musical theatre program as well as the Bloomington Playwright's Project. Purdue is also about an hour away and does nice work as well.
I'll echo the recommendation for the Phoenix. Know No Stranger and ShadowApe are both groups that do more avant garde or inventive performance pieces. IRT indeed does safe productions, but their resources allow them to consistently do good work with beautiful set design and top notch casts.
Butler University has a pretty strong performing arts programs and some of their theatre productions have been quite good. The Cabaret brings in amazing artists in a beautiful intimate space for fare less than the price of a comparable show in NYC.
Our location also is great for quick trips to Cincinnati (Playhouse in the Park), Louisville (Humana Festival of New Plays), and the vibrant theatre scene in Chicago.