A place that I really like although it is closer to UT than downtown is El Mercado at 17th and Lavaca. I haven't been there in a year or so but there are usually lots of fans there before the game. They also have tvs all over so that you can keep up with the games. Also, they used to run a shuttle van between the restaurant and the stadium. As someone who dearly loves San Antonio mexican food, I have to say the food is pretty good.
I really like that little Mexican cafe called Las Manitas between 2nd and 3rd on Congress. They have good food plus you always see famous people in there.
Go and grab a steak at the Hoffbreau on west 6th street. Great steak served in 1/4 inch of melted butter, along with huge slabs of fried taters. Mmmmm....