Recently moved to Indianapolis. Appears to be overrun by chain restaurants....
Yes, we are unfortunately full of chains. However, we also have some pretty talented chefs. For non-cain recommendations, you'll have to give us some ideas as to what you are looking for.
Indianapolis Monthly has a decent listing of restaurants, but it seems to me that they are focusing more on the Carmel, Fishers area more that true Indy these days.
I thought the same thing when I moved to the area from the West Coast - my fiance (now husband) still remembers my comment that I had never seen so many chain restaurants lined up on most of the main streets.
The Broad Ripple area has many small, independent restaurants.
The Music Mill has an excellent restaurant and hosts musical acts.
Look closely at some of the ubiquitous strip malls - many have hidden gems in them. Losts of good ethnic choices. My favorite is Taste of Thai in Castleton, in the same center as Trader Joes.
Downtown - hit Massachussetts Avenue.
At the Circle Centre Mall downtown, Bertolinis is very good Italian - yes, it's a chain but there are only 4 nationwide!
For decent upscale chain restaurants, head to Clay Terrace in Carmel - Kona Grill, Mitchells Fish Market, etc.
Everything I've mentioned is on the Northside and Downtown; I'm unfamiliar with the South and West, except for Rick's Boatyard near Eagle Creek Park - nice place.
This blog reviews Indy restaurants
There are a couple of other posts on htis site for good Indy food -- do a search and see what comes up.
But quickly, for nonchain upscale try Elements, Oakleys, L'Explorateur.
A little more casual but aslo very good is R bistro.
Also good ethnic Just for example, lately we've had good Mexican at El Maguey and good Vietnamese at Saigon. But there are lots of options. Check the Indy Monthly too, and subscribe to their weekly email newsletter The Dish.