Overall - Dream. But someone who was born here - Carl Lewis. He was a world class athlete. He was just amazing. If you threw out my bias toward the Rockets, then it would be Carl Lewis in a landslide. He came to my elementary school once with Mattress Mac, that was awesome.
Look, I know that Jeff Balke helps run an amazing website and he was instrumental in keeping the Rockets in Houston, but best ATHLETE?? That's stretching it a little.... Maybe he wins the poll for best Houston musician...wait...nope, that goes to ZZ top! Sorry Jeff, but you're just one big loser!
I know the question asks for best, but my heart for some reason goes with Warren Moon. He isn't the best, but he's my favorite.
He did pitch one year at Dulles High School before he went to Spring Woods. A very good bio of Clemens can be read here: http://rocketroger_clemens.tripod.com/bio.html