If you have cash to burn, St Elmo's Steakhouse is the best place in town, IMO, but you will drop a ton of cash on it.
Rock Bottom Brewery is a great medium priced meal with a wide selection of good brews.
Acauplco Joe's has great Mexican food.
Le Peep's is a great breakfast place. So is First Watch on N Illinois.
Claddagh Irish Pub also has great food and a great selection of drinks.
If you want to laugh, you could try Fogo de Chao which brands itself as a Brazillian Steakhouse and tell us all the ways that it is wrong!
The Old Spaghetti Factory has some pretty solid Italian for a good price. So is Bucca di Beppo but that is all "family style" dining and the portions (and price) are big.
Don't know if you are coming with kids but the Children's Museum is world-class.
The Indianapolis 500 Motor Speedway Museum is also a must see on your first trip to Indy.
Christmas lights at the Indianapolis Zoo is pretty nice the first time you see them. The 20th time? Not so much.
If you want to drive 2 hours to the east, I could show you around the Air Force Museum in Dayton, OH at Wright Patterson Air Force Base if you are interested in airpower.
I don't know if they are doing a Christmas show at Conner Prarie living history museum but if so, that would be a great look at some history of North America.
Walk Worthy,