Hmmm... I'm not sure. I do know that the Sonic here in Bloomington (about 50 miles from Indy) closed a while back. Maybe the company is having some trouble or something.
I'm sure you have spent time in the downtown area, like around Circle Centre Mall and stuff, right? Circle Centre has a Johnny Rocket's, you would probably like that if you can't find a Sonic. Back when I ate meat, I seem to remember REALLY enjoying their burgers.
They are a little pricey, but the '50s diner atmosphere is kinda cool. There are also a ton of local breweries around there, and the Ram brewery has really huge burgers (and veggie burgers for me
). The food there is really good if you're willing to spend a little more. Have fun on your vacation!