The only mountainous terrain I’ve ever seen in Texas would be in the vicinity of El Paso, far west. There are areas with decent sized hills, Hill Country. That’s the prettiest to me as an NC native. It’s dryer than here and less green, but it’s got a hint of California with the live oaks and wildflowers, so it’s very pleasant to look at, especially when the blue bonnets are blooming. The rest of Texas strikes me as a little too brown unless you’re way east or down along the coast, and then you hit the heat and high humidity that is worse than summers here, but theirs is practically year-round.
Never been to El Paso. If one is not about the humidity, I would stay away from Houston. Dallas area is not so good either. The Panhandle is really dry...Amarillo. Having lived in all of these areas, I would not want to live anywhere but Texas. Having said that, there are lots of places to choose from. You want a beach, like Basil said, go to Galveston.
Georgetown is very nice.