RUB BBQ pub is a good place for BBQ, there is a bunch of little Caesar chain stores around too. Hockeytown Cafe has some good sandwiches and if you want something fast get a sandwich at Jimmy Johns.

There are some good Greek gyro and pita places in Greektown a few blocks away. There is also subways, Little Caesars, McDonalds and other fast food by the stadium and then places like Hockeytown Cafe and Cheli's Bar which are focused on hockey but still fun.