In college a buddy and I made trip down to Big Bend and explored the countryside. We stopped in Lajitas and bought 6 pack of Lonestar and a bag of cheetos for the mayor Clay Henry III (a goat). He drank every last drop and almost ate the cheeto bag.
One day I saw on the Texas map that FM 170 ends northwest of presidio at the town of Candelaria. So we decided to go the end of the road for the he!! of it, and we stumbled upon the Chinatti Hot Springs. It is one of the neatest places I've ever been to!!! Literally an oasis in the middle of the desert. Up the road from the hot springs (Ruidoso TX) is a cantina that is generally closed but the caretakers will make a phone call and get it opened for you.
There is a ton of history in that small area... The remains of Ft. Ruidoso can be seen (built during Pancho Villa's raids). The only free-standing 2 story adobe church in the state is right there. There are cliff dwellings all over as well. Here's the link
http://www.chinatihotsprings.com/Home.html
Also, if you do make the trip accross the border to "OJ"... Check out Peguis Canyon, it's the largest canyon in the Big Bend Region. Here's a picture of it.