Dunno if you have already gone or not, but if not...
Indianapolis is a pretty family oriented city, so you won't really find a mindblowing nightlife scene there. But your best bets are going to be downtown, Broad Ripple, or Fountain Square.
You can go to White River State Park, walk along the canal, visit the Eiteljorg Museum, NCAA Hall of Champions, and Indianapolis Zoo.
Indianapolis Museum of Art isn't too bad.
Obviously, there is the Indianapolis Motor Speedway and if you are out that way, you can also check out Eagle Creek Park.
If you can get up early enough, go to Long's Bakery. They have some of the best donuts on the planet and they sell out early.
Other places to eat might be Yats or St. Elmos Steakhouse.
If you have more time and willing to drive further out, both Brown County State Park and Turkey Run State Park are worth a visit.
