Casa Navarro in particular, but generally the whole Mexican historical sights. Those and some of the parks are supposed to be good; Pallo Duro Canyon and McKinney Falls.
The Palo Duro Canyons are amazing.
I've never been to McKinney Falls, but I'll have to plan a trip there now that you've tipped me off.
If you want to spend a long time in one park, you could check out Big Bend, but it gets ridiculously crowded around Spring Break. Big Bend is probably the best place to just ride around on a motorcycle in all of Texas.
http://www.big.bend.national-park.com/
I personally prefer Guadalupe Mountain National Park, just because it's not as crowded, and I think the views are much better.
http://www.guadalupe.mountains.national-park.com/
And, Carlsbad Caverns are just a hour or two away from the Guadalupe Mountains (not Texas, but the one hour tour is well worth it).
http://www.nps.gov/cave/
I've wanted to go to the Davis mountains for awhile, but haven't made it yet.
http://www.tpwd.state.tx.us/park/davis/