Nice (and pretty close to each other) places to go...
San Antonio, Galveston, and Houston Texas.
San Antonio has the Riverwalk (which is lots of fun) and the Alamo.
Galveston has the beach (we were there in early January, still a bit cold to swim, but we were wading above the knees), the Lone Star Flight Museum (which was really great, and not too bad costwise I think it was $8/adult?), the harbor tour (well worth it at $12/adult, we saw lots of nifty stuff including dolphins). There's also a tourist-oriented water-park, zoo place - but it was too pricy for those of us saving for a wedding
we were going low-budget. Note - skip the train museum... it sucked a lot.
Houston has the NASA space center - which I haven't been too, but I've heard lots of really good things.
If you're the pack-as-much-into-your-trip as you can type... Flying into San Antonio or Houston and getting a rental car, you could easily do all this stuff in a week.
Jeremy and I flew into Dallas on a Thursday morning (9 am arrival), got picked up by our family in Dallas (they drove down since they had more vacation time). From Dallas we drove (4+hours) to San Antonio and did the Riverwalk and the Alamo. Next morning, we drove to Texas City (between Houston and Galveston - don't stay there... oil refinery stinkyness, plus it wasn't the greatest place). Unloaded our stuff, and drove to Galveston and played at the beach, had dinner. The next morning we had been planning to go to Houston, but we decided to do more stuff in Galveston (Lone Star, Train, Harbor tour, shopping). So in two and a half days - we crammed in a lot of stuff, and all of Jeremy's treatments (one nice thing about road tripping - car time can be neb time).
-Michelle