If you've got time, dowtown Indy has lots to offer:
Indianapolis Zoo/White River Gardens (great for photos)
Eiteljorg Museum (Native American works)
NCAA Headquarters/Hall of Fame
The best seafood can be had at The Oceanaire Seafood Room...the only place in Indy that I trust to eat raw oysters (I only eat them in locations where a large body of water exists) Kinda pricey, but great food!!
A little ways out of downtown is the Indianapolis Museum of Art, the Children's Museum (I have such a better time going as an adult than a kid!!), and an artsy area named Broad Ripple. If you go to Broad Ripple, you must have a meal at the Broad Ripple Brew Pub...try the scottish egg!
There's also Crown Hill Cemetery, a little north of downtown, near the art museum. It's the 3rd largest cemetery in the US with lots of history and beauty. Photographers enjoy taking pics of the old statues near the graves, or the Gothic cathedral in the center of the cemetery. If you head up the hill to James Whitcomb Riley's plot, you are on the top of the hill and can overlook all of Indy. Very pretty in summer and fall!