A thing I like to in Indie, although not technically Gencon related:
There's a restaurant around the corner from the Omni called the Red-Eye Cafe. Food is pretty decent, they have a pretty decently stocked bar, and they're open 24/7. If it's 3am, and you're in the mood for some waffles and a tall Blue Moon, that's the place to go.
Also an Indie fave (for me anyway). The RAM brewery. I technically didn't discover it, but they brew their own beer on-site, and it's pretty good stuff too. Get a growler of whatever strikes your fancy, they have a pretty good variety, and the growler makes a nice souvenir.
Bring enough liquor to last the weekend. I ran out halfway through the con last year, and decided to walk to the nearest liquor store. Problem is, you have to pass through a rougher part of town than most of the hotels and restaurants are located, and I ended up getting chased by a street person yelling gibberish at me. Makes an interesting story, but I found the experience unpleasant. Also, the guy at the liquor store is an ass and gave me hell about everything from my credit card to my ID to my signature.