You have some climbing nearby at Kings Bluff in Clarksville. It is limestone and not as good as our splitter sandstone here in the south. If you want better stone to climb on, check out the climbing throughout the Cumberland Plateau and Chattanooga.
Go to king's bluff, you can make it there every day after work if you're on base. Unfortunately, most of my old climbing buddies are overseas right now, but if you head out there on a good weekend look for the locals, or really anybody. As long as you're not an incompetent, you shouldn't have trouble finding partners. You can probably convince someone who's there to go on a road trip with you. It's not too hard. If none of the above works, go to climb Nashville. Repeat.
Source: spent 5 yrs on ft Campbell; ~100 weekends climbing at KB.
Edit: if you have a car and can't get anyone else to go, go to RRG, T-Wall(for trad) and the Obed ( stay at dell and Marty's lily pad campground) if you can't find a partner at any of these locations.... Well then there's a good chance MP won't be able to help you either.