Already multiple quality schools have been mentioned.
If New Orleans is not too far away, I would add Tulane to the pile. It isn’t as selective as Rice but its rep is pretty strong. It’s a pretty campus in a beautiful section of New Orleans. If you’re in East Texas, the drive might not be too terrible.
Anyway, it would be a good mid-sized private university option to fill the chasm between, say, Rice and SMU.