The countryside around the town of Fort Davis is beautiful. The Davis Mountains are gorgeous, and the vegetation is quite different from what you see in Big Bend National Park, with more little trees, mainly pines, and lots of huge granite boulders. The only downside of visiting this area (and 95% of Texas actually!!) is that every piece of land is private and off-limits. So you can only admire from the roads! There are probably ranches that accomodate tourists, but I have not been to one.
This country is, however, ideal for road bicyclists!!
Finally, for a breath-taking view of the Davis Mountains, drive up to the McDonald observatory.