If your concert is at the Murat, you are in luck. It is located on Massachusetts Ave., on the northeast corner of downtown, which is one of the better dining destinations in the city. You can see a complete guide to restaurants on this site:
http://www.discovermassave.com/
Elements would be my number one recommendation. I've also heard good things about R. Bistrot, but haven't eaten there myself. The Scholar's Inn is solid, with excellent breads and baked goods. If you are in a hurry, grab a quick plate of whatever they've got on special at Yats (cajun/creole). I think Agio is over-rated, so recommend avoiding it.
St. Elmo's is justly famous for its shrimp cocktail and atmosphere, but for steaks this is one of the most over-rated places in the country, IMO. The meat is not up to top steakhouse standards. What's more, it isn't even easy walking distance from the Murat. The same goes for the Oceannaire, which I found to be a serviceable but undistinguished and pricey establishment. What's more, it's a chain. I'm sure you'll be able to go to one in Louisville soon, so why bother making the drive to Indy for that? The entire Circle Centre area is chain restaurant row, and Indy in general is a very chain dominated dining town.
Please note that parking and traffic on weekend evenings can be a drag on Mass Ave., so leave yourself plenty of time. Plus reservations will be a must in most of these places.
Incidentially, the Murat Temple is my favorite building in the city.