Ignore the rude guy.
I live in Austin so I can not tell you where to stay, I am sure one of the other posters will be able to help you out. If not use citysearch.com and they should have info on the night life.
Inn At The Ballpark, Four Seasons, or The Hilton Americas are all nice and very close to Minute Maid. Most of the nicer downtown restaurants and entertainment venues are close as well. Our downtown area is very small compared to Chicago, so nothing is going to seem far away to you.
When I get to work in the morning, I'll see if I can post a few links.
This site has a lot of links to entertainment\food\arts\etc
I, for one, hope you are treated the same way I was treated in Chicago as an Astros fan.
If so, you'll have a great trip. I only caught mess from one guy, and the rest of the fans and town were great.
The past two trips I've made to Houston from Arkansas I went on Priceline and ended up at the Hyatt both times for 50 bucks a night. Super rooms for 50ish a night. Walking distance from the park. I know there is a bar or two around the stadium. Can't remember which one we went to but it was three letters.
Here's another nice hotel near the ball park. They have about ten locations around the world and I've stayed in the one in Manhattan recently. Very nice.