If you are planning to be in the Ft. Davis area, then check out http://www.peytonsbikes.com/ftdavis.htm
for some routes in the area. However, virtually any of the paved roads in the Marathon, Alpine, Ft Davis, Big Bend National Park, etc, are good low traffic roads.
I particularly like riding in the National Park. The scenery is unbeatable. For an incredible ride, start at the park headquarters at Panther Junction and ride up to The Basin in the center of the Chisos Mountain Range. the climb starts steep and just gets steeper the further you go. You can get lunch at the restaurant in The Basin and it's also where the park motel is located. The trip back is pure joy.
Check out bicyclebigbend.com as well.
There's plenty of other good riding, but be sure you have plenty of water as sources or water can be many miles apart. Also, there are lot's of hills and the grades can be deceptive.
And, if you have a MTB, bring it along. Plenty of great MTB riding in Big Bend!