Visit the San Jacinto Monument in Deer Park.
This monument really took me by surprise when I first visited it. While standing and looking at the monument you get the feeling that the whole design of the monument and the grounds around it are a take on the Mall in Washington DC. It has its' own reflecting pool and everything. The guides in the monument will be the first to tell you however that it stands a full 12 feet taller than that Washington monument does. Indeed, Guinness lists it as the tallest monument column in the world. In the base of the monument is an EXCELLENT museum describing the events from the Alamo and beyond, leading up to Sam Houston's defeat of Santa Anna in San Jacinto. There is also a very good film on the history of the Texas Revolution. Whether or not you wish to go to the top of the tower is up to you, but the view is not all that great.
There are not many places that you can go to see a battleship anymore. You can see the USS North Carolina in Wilmington, the USS Missouri in Pearl Harbor, and the USS Texas in Deer Park. I have seen all three, and this one was a real treat. In the first two ships many of the areas were sealed off permanently to visitors. With the USS Texas that is not the case. Here you can climb into the main gun turret and explore the ship at will. You can climb the superstructure just about as high as it will go. This ship was built during WWI and saw action through WWII. It was present for Iwo Jima and Okinawa. Another fact is that this ship and the harbor it sits in was used extensively in the recent movie 'Pearl Harbor'.