I often go to DCA, ATL, LGA, MSP as they are direct flights from IND.

MSP - light rail pick up at airport; takes you directly to Mall of America and downtown.
ATL - MARTA station at airport; hit the touristy stuff near Centennial Park
DCA - METRO station at airport; Smithsonian, Zoo, Arlington, National Monuments are all free.
LGA - taxi rides are expensive; NYC is always fun to visit. Took the kids to skate at Rockefeller Center last winter.