How far are you willing to drive, and what part of the state are you departing from?
Justin and I have done one long Texas trip towing a trailer (a small, rented pop-up) -- San Antonio to
Big Bend National Park. We went in September 2001 -- it would be cooler and perhaps stormier in late November, especially in the Basin area.
But any place in Texas is fair game, depending on what you're looking for in terms of temperatures, entertainment, recreation and driving time.