I believe MOAB rents bikes (Murfreesboro area) and Cumberland Transit (Downtown/Vandy area Nashville)
Not knowing your skill level, I'd recommend Chickasaw Trace in Columbia, TN as it is probably the best marked trail in the area. It also offers beginner friendly sections (River and Woodland trails) and more intermediate (Black Hills, Trail of Tears). The total length is just under 10 miles of trail.
Checkout our message board closer to that weekend and we should have a ride or two posted. You may have trouble renting a bike in Murfreesboro as our 1 local shop does not rent. It's possible you might be able to borrow a bike from a club member. What size do you ride?
We are about 30 miles south of Nashville off of I-24 East.
I ride a medium men's frame - both mountain and road. Thanks for the suggestions. I'm only going to be able to ride during the day Friday due to other committments the other days. But, I'm emailing bike shops, downloading trail maps and using the heck out of mapquest to figure out if I can make something work. I expect you guys have some fun trails - road and mtb.