Do not stay near UH, it is in a very bad neighborhood. Stay either close to downtown, the Museum district, Rice (West U), or the Galleria.
Washington corridor is the "in" bar scene now. (just northwest of downtown.) Many good restuants and bars(beavers, Tap house, Catalan, Dark Horse, etc.)
For bars not on Washington, Anvil is excellent for those that like well made cocktails and cask beer, near there for a alternative crowd with good drinks is Poison Girl. I like under the volcano also.
For food not mentioned, Stella stola is great, as is Haven. you cannot really go wrong with The breakfast Klub, Taste of Texas, Papa's Bros Stakhouse, or Moe's a place for steaks. Feast is widely considered the one of the best new resturants in the US.