Hey Dan, I spend A LOT of time in Indy, but unfortunately, I'm not allowed to just offer up "willy nilly" my sister's kitchen for some of the best food you'll find there.
I second Patachou, and loudly. I also love Three sisters, but it's in Broadripple. Three sisters is comparable to Meridian Cafe in atmosphere, so it might not suit your dining mood, but the food is incredible. As cheesy as it seems to talk a place up based on the merit of their Food Network exposure, it was discovered on DDD, and I wasn't surprised at all when I found out.
What I DO think you would love: Sun King Brewery. It's located somewhere downtown (an area I'm totally unfamiliar with so far). My Brother-in-law works there, so I've gotten to drink a shit-ton of their brew - all delicious. But don't go too thirsty or hungry. Why would I say so? Because they don't serve food or pints. They do, however, hand you tickets for four beer samples. You walk in, get the tickets, walk to the growler trough area, and get your 4 free 4 ounce tastes. They have a huge selection of growlers and coolers full of 16 ounce cans if you decide to buy. It's a huge warehouse kind of place, too, with lots of retail items and milling patrons with tall boy tables, so if you don't buy their beer after drinking their free samples, it's not uncomfortable to say thank you and find your exit. At least not in my experience. Their beers won several blue ribbons at GABF this past year, and they're being paraded already as Indiana's favorite brewery in some circles. They've only been around for 2 yrs or less (we 1st discovered them at Indy's winter fest 2010). Holler at me if you go to let me know whether or not I'm right on or just Over-Zealous.