First, get into some Texas music, just to set the mood.
http://youtu.be/GKeDcF1v_Y4
San Jacinto Battleground State Historic Site, Laporte TX. (Too close to Houston, avoid the freeways, take the back roads.) This is where the Texians got revenge for the Alamo! Home of the San Jacento monument, go to the top and look around!
The main attraction is the Battleship Texas, book your trip ahead, reserve the "Hard Hat Tour", a guided tour to the inner works of a 100 year old dreadnaught battleship. Guarantee you will be amazed!
Just down the road, Galveston, Sea Wolf Park, see the USS Cavalla, WW2 submarine. Go inside, just imagine...
There is also an Immigration museum there. Galveston was the last stop for the ships bringing the immigrants from Europe. Ellis Island was the first stop, if all your paper work was in order, you were not sick, and they liked your looks, you got off the boat. If you were "less than desirable", you went on down the east coast, given many opportunities to go ashore. If you were still on the boat when it hit Galveston, well you were at the end of the line, everybody off... Just take a look at what some of these "rejects" accomplished!
And there is the Ellisa, also in Galveston, Texas Seaport Museum. An 1877 tall ship, see what life at sea would have been like, when boats were made of wood and men were made of steel!
Couple hundred miles down the road in Corpus Christi, beautiful clean beaches! Tour the USS Lexington, aircraft carrier. Lots of planes to see, takes a day to see the whole ship, it's HUGE!
If you get out west, check out Big Bend National Park. Only 800,000 acres to explore, so take a canteen! It's desert wilderness, go in the spring, beautiful flowering cactus... Lots of cactus! Go in the summer if you need to be properly thawed, if you're lucky it might hit 117*!
Well, this is getting long, I been here all my 59 years, still ain't seen it all, so plan on staying awhile. You got lots to see!