The Unitarian Universalist Church in Indianapolis hosts the Indy Folk Series, a monthly folk concert by regional and touring performers held on Saturday nights throughout the year. The music ranges from folk to bluegrass, and they have brought some great acts into the region.
You can explore their event schedule at http://www.indyfolkseries.org/. They are located at 615 West 43rd Street in Indianapolis, and you can map their location here.