When you coming?
There is always Weber Grill which is by Circle Center mall downtown, There is also PF Changs in the mall and the Ram which is a brewhouse on the backside of the mall on Maryland Street I do believe and is right across from St Elmo's. If you are looking for fancy there is also the Eagles Nest which is on the 24th floor of the Hyatt downtown. I have also heard great reviews about the old spaghetti factory.
Depending on when you will be in Indy on June 14 there is Strawberry festival on monument circle which is put on by the Christ Church Cathedral church and for 6.00 you can get strawberry shortcake with ice cream and whipped cream and they usually put out over 18,000 shortcakes on that day. I work with one of the guys who will be working on that day and we are planning on stopping there after our team lunch at PF Changs that day.
Here is a link to the Strawberry Festival