The man to talk to would probably be Alan. He is BigTEX on here. I just sent him a PM to come in here.
Just off the top of my head I would recommend the world famous 'Menil Collection'. I have friends and family come down from NYC just to see this collection. That's just the beginning. Home Houston has a world class art scene that is well know OUTSIDE of Texas. Go figure.
+1 for the Menil collection. One of my favorites. If you go there, you'll be on the edge of the Museum District with many more art museums close by.. The Jung, Contemporary Arts Museum, and Museum of Fine art. Plus many other museums, Hermann Park/HMNS, and just lots of cool stuff to do in the area. I believe there are many galleries in the area, but haven't really explored the buying/selling scene there. If I had to guess, there are a lot of art collectors in Houston.
I didn't care much for the Menil collection. But the Museum of Fine Arts is good. Not perhaps to the standard of DC/NYC/Chicago but good.
He is asking about galleries, NOT musuems. Yes to Colquitt, and a few more on Montrose, those are the areas surrounding MOMA and MFA. Maybe the guy to check in with, Ross....would be my art framer, Chris Lesikar, who owns FrameTek. A Google will bring up articles about him and his business, and I would guess he knows everyone worth knowing in town!! Be gald to help myself of course, there are tons of smaller galleries scattered thru River Oaks and the Heights too!
Photography, painting, statues? Start at colquitt as has been mentioned. Also check out "off the wall" in the galeria.