If you have a lot of travel time and are a fan of history you might enjoy taking the Old Spanish Trail (OST) which extends from St. Augistine to San Diego.
I agree, because I like taking back roads on long road trips. However, I would not blindly follow the map but without checking the big urban areas very closely.
For example, in the stretch of the Old Spanish Trail extending 20+ miles either direction from Houston, the roads labeled Hwy 90, 90-A (for alternate) or O.S.T. are not appealing to the tourist. There is no natural scenery to speak of, as 100+ years of development (and steady decline that followed in some areas) has created a thoroughly urban landscape. The once-quaint "travel court" from the early days of automobile travel is often a modern-day flop house.
Houston itself has some interesting big-city attractions: very good museums, Rockets games, the Williams Tower water wall, etc. The NBA all-star game will be here February 17th, with open-to-the public street parties an a convention center "experience".
By coincidence, while in Austin this weekend I saw a TV travelogue for day trips outside Houston. It listed some options along the bay between Houston and Galveston. Space Center Houston and several restaurants are included.
Video: Kemah, TX | Watch The Daytripper Online | KLRU Video
I see they have other shows on South Padre Island and the Beaumont area, but I couldn't get them to load. The one from Beaumont area had headlines suggesting it was heavy on nature exploration at Caddo Lake or in the Big Thicket Nature Preserve. I think early March would be the perfect time weather-wise to see a swamp / bayou environment from a boat, if that interests you. Sadly, it's a bit too early for storm chasing:
Extreme Tornado Tours)
This travel guide was written by a well-respected Houston journalist who hosted a long-running TV travelogue called
The Eyes of Texas. It's dated for restaurants and attractions, but would be very good for natural or historic places. Cheap, too.
Amazon.com: Buying Choices: Ray Miller's Eyes of Texas Travel Guide: Houston/Gulf Coast