Mexican - Gueros (Austin Institution, trendy, not fancy), Matt's El Rancho (further from downtown, but can accomodate large groups).
Hamburgers - Casino El Camino on 6th. Also, you can get your drink on a little early there.
BBQ - not a lot of great BBQ in the city. Iron Works is downtown and pretty good.
If you just want to start downtown and not have to cab or drive it at all, Iron Cactus on Sixth is pretty good as well.
Lots of places to go -- For a group of 8, I'd probably do Gueros if I had a van/could hop in cabs, followed by Iron Cactus and th Casino El Camino.
Of course, there is always Hooters. . . . .