I stayed in that Hilton last year during my first and only trip to Minute Maid. It's a nice hotel and about 2 easy blocks from the ballpark. There's a walkway in the convention center section of the hotel from which you can take a really nice picture of ballpark... much better than the view from the guest rooms on that side.
I can second the notion that it will defintely be hot there compared to Ohio.
Downtown Houston is deadly quiet on the weekends, at least compared to San Antonio. Among the few non-quiet areas is the aquarium, just a few blocks from the hotel. It's about 3 years old and run by the Landry's Restaurant corporation. (Joe's Crab Shack, Rainforest Cafe, etc.) I haven't been there, but have heard it's nice.