It’d be a few hours drive, but the trails around the University of the South in Sewanee, Tennessee are great for mountain biking/hiking. The perimeter trail is ~ 20 miles in length. It is mostly remote, in the woods, up and down, some rough spots - it is not a smooth, high speed trail. I did see a rattle snake there once (heard it rattling first). Here’s the map: http://visit.sewanee.edu/_media/pdf/hiking.pdf
Drive past the equestrian center, park car off the dirt road somewhere, unload bikes, go riding – or go hiking. Actually you can park ANYWHERE to start your bike ride - near the big white cross is good, or anywhere on the campus is good. I did it many times and no one said anything to me and there was no red tape. The University campus is very beautiful - good for biking also. A great bike shop called Woody’s Bicycles is in Sewanee and right across the street is a pub with good food and beer. http://www.woodysbicycles.com/web/Welcome.html
You might try the drive south from Winchester, Tn to Hytop, Al along Rowe Gap Road for a rural scenic drive. There is some hiking along there near the TN/AL border to a place called Walls of Jerico or something like that - I have not hiked it. http://www.alapark.com/press/release.cfm?id=322
For a weekend getaway, you can go to Bryson City, NC and rent a cabin from Galbreath Creek Cabins. I’m cheap (usually will sleep in my car when traveling if no CG is available, rather than spend $$ for a Motel 6) and these cabins seemed expensive but were well worth the money and we did not want to leave. http://www.galbreathcreekcabins.com/our-cabins.html
I recommend the Treehouse or the Smith Mill Cabin – the only ones I am familiar with – just big enough for 2 people – larger cabins are available. Drive a few miles thru the woods to nearby Deep Creek to rent inner tubes for some mild almost-white-water tubing. http://www.greatsmokies.com/tubing.php
Or go to GSMNP and go for a hike or scenic drive. Do drive the Blue Ridge Parkway toward Asheville, NC - very beautiful drive. Good food in Bryson City.
Or, for hiking/camping go to Mt. Mitchell State Park in NC. http://www.ncparks.gov/Visit/parks/momi ... arkmap.pdf
Hike/bike trip: Lock bikes at the top of Mt. Mitchell, drive car down to Black Mountain campground at the bottom of the peak and hike up to the bikes, for ~ 3,600’ gain. Then, put on sweatshirt and windbreaker, and ride back down to the car. Part of road to CG is gravel, so mountain bike would be best. I did it on street bike and wanted mountain bike. It can be very cold on top and may be windy so bring warm clothes. Can also backpack overnight along ridge starting at Mt. Mitchell summit/visitor center.
Mt. Sterling area in GSMNP is a good weekend hike. Hike up from Big Creek CG, camp near the lookout tower at the top. To do a loop, hide bikes in woods near Mt. Sterling Gap (just a wide spot in dirt road 10 years ago), drive back to Big Creek in car, hike up to Mt. Sterling, then hike down to bikes at the gap and ride back to car being VERY cautious if you ride with a full pack – when I did it 10 years ago the road was good gravel – best on a mountain bike – tricky on a road bike. http://www.hikinginthesmokys.com/mountsterling.htm
Here is better map, Mt. Sterling is in upper right of map: http://www.nps.gov/grsm/planyourvisit/u ... uly-11.pdf
Have fun. Watch for snakes. Pull the ticks off if they are stuck on you. Probably will not cause any problems. People who go outdoors back there will be bitten by ticks hundreds of times in their lives with no ill effects. Learn about and avoid chiggers – they leave a miserable, itchy bite.