It's an old thread, but my contribution is: 

Loughmiller's Pub and Eatery 
Walking distance north of the Convention Center
My favorite: Pepper Jack Stuffed Pretzels
2 soft pretzels filled with pepper jack cheese and deep fried. $10. 

And also thank you to the other posters, I'm making a little guide book of places to eat and these are great suggestions. 

Good stuff here.

I'll just add:

Thai Paradise   (Market St, 1.5 blocks west of Monument Circle)

I recommend Harry & Izzy's. Excellent service, and a wonderful experience --  a bit expensive but it was nice to get away and relax the mind. 

Stay with me here: They use the same kitchen as St. Elmo's, according to industry experts in the area. 

The difference? I thought having lunch at Harry & Izzy's was very nice, both in interior and service, but they toned down any perceived pretense for lunch and possibly better prices during the lunch service? 

TL;DR: Excellent food, service, drink menu; Highly recommend. 

ALSO Recommend: The Oceanaire Seafood Room
Slightly pricey, but an evening chill out in a dark, elegant environment with excellent service was very nice before heading in to that evening / late evening event. Excellent oysters, sea options, and beasts from the land as well.

TL;DR: Dark, elegant, inviting, food and drink options, service; Highly recommend
 

The places that I will miss dearly this Summer are;

Pearl Street pizza, for their deep dish. The veggie deluxe with chicken and jajapenos added is my jam. Also, they have a pear and gorgonzola that is simply great.

First Watch for breakfast. I don't eat red meat, and the fact that they have both chicken and turkey sausage links/patties is amazing.

Eagle Tavern (Across the street from Basbeaux) is some of the best fried chicken that I've ever had. Homemade biscuits and jam, and the finest mac7 cheese that has evwer passed my lips. 

Hell, I might go to Gencon for the food moreso than the games at this point...:D

I hope most of the places are still around next year!  So many good places to eat in Indy.

Any places have a good beer tap list? Last time I went, I went to Tow Yard Brewing but it closed.

EDIT: Just Google'd and saw a new place Ellison Brewing opened in the same location.

By next summer, this list might be totally invalid.  Restaurants/bars are not stable at the best of times, and this year.. well.. :-(

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I've been to Ellison a few times. Aaron knows what he's doing, his 1st location was opened in Lansing years ago.