Andy, if you have a little time on hand, there are a couple of ways to travel besides flying. It's rather inexpensive, too!
1. Take the Amtrak train down to New Orleans, party there, then take another one or the Greyhound bus from N.O. to Houston.
The Crescent is the one you want to look for from NY to NO, then the Sunset from N.O. to Houston.
2. If you have an extra day, I would suggest that you take the Amtrak down to Jacksonville Florida (the Silver Star). There's no train service for a certain trek between Fla and TX, so you will have to take the Greyound bus to Houston.
Also there's a six-mile distance between the train and bus station in JAX (about 6 miles), but there's enough time in between, you can even walk from one to the other, LOL!