Agree with everyone so far with one exception:
Hung Fong is not good Asian. Van's, nearby, is a little more pricey, but *far* better. Mon's Thai Bistro on Broadway is fantastic, as is Tong's Thai on Austin Highway. However, none of them are in a location close to downtown.
If you are downtown and want something different from the Riverwalk, Southtown is fun. Rosario's is the go-to place for Mexican. The Guenther House/Pioneer Flour Mill does an excellent brunch and is nearly at the end of King William Street. Blue Star Brewery is a great microbrewery at the Blue Star Arts complex. (Honey, you can go look at art, I'll make sure the beer stays cold over here.
) Avoid "La Focaccia", it's the worst Italian I have ever had.
Don't go east of 281/37 downtown. They have the overpasses lit up like Christmas in rainbow colors so the poor tourists don't know they are being guided into the ghetto.
If you are looking for Margarhitas, The Naked Iguana has the best happy hour on the Riverwalk, with huge margies for 7$.