The Ram down town is really good also, if you arent looking for anything really upscale. Great burgers also. I live in Speedway, near the track so I'm a bit biased in saying you can't come to Indy with out going to the Indianapolis Motor Speedway. The museum is great there, plus seeing the track and realizing how big it is is pretty cool.
I highly recommend Long's Bakery on 16th St. or Southport Rd. The best donuts in town. Mmmmmm .....<drooool>.... donuts..... (they also have some killer pastries.)
I live up in the corner not far from Chicago. I would much rather do a weekend in Indy. Great downtown, hotels, restaurants, bars and people. As it has been said before-Chicago sucks!!!
The Children's Museum is NOT gun friendly, and the Zoo is not entirely friendly. They will not allow you to carry into the Zoo as one person attempted to do several years ago, and it created too much of a distraction/disturbance with most of the "Mommies" there.
The Indianapolis Museum of Art is an absolutely wonderful place, and is FREE admission. Depending on when you are here, their gardens are spectacular, too.
The State Museum is not too bad.
For fun stuff, you could go ice skating at the PanAm rink downtown. Head north and check out Zionsville. It's a pretty neat attraction with it's historic brick Main street, and cozy shops.
Plenty of good restaurants and coffee shops all around, although Indy is fairly lacking on truly good bakeries.