There are a lot of places to play of course, but I think there are only really three 'action' type places that I'm aware of, by action I mean places where just about anyone can walk into and get a game, etc.
Bogies Billiards - it's up on the north side of Houston
Big Tyme Billiards - it's about a mile or two from Bogies on the north side
Legends - this place is over in the Southeast end of Houston in League City.
There are numerous other places of course, and many will have action at times. Slick Willies has several locations in town, Fast Eddies, etc. But to my understanding the three above are generally considered the 'big three' for action.
You can Google any of them to find the actual address and location in relation to where you'll be staying.
Hope this helps?