Thats where Im from. Check it out
East Tennessee and a good chance to see snow
The Great Smokey Mountains National Park http://www.nps.gov/grsm/index.htm
This is a great place to be in the mountains especially if you are taking your kids. If I were going here and you are driving I would take I-95 all the way up the coast until you reach I-26 in Georgia. Follow that to Ashville, NC. From Ashville North Carolina go to Maggie Valley NC http://www.maggievalley.org/
Take the road straight through town and you will end up in Cherokee, NC. This is home of the Cherokee Indians and a great place to learn about the Indian culture. From Cherokee, NC http://www.cherokeesmokies.com/
follow the road through town and go up into the Smokey Mountains National Park. (Both Maggie Valley and Cherokee are 1 day trips. Meaning you can see or do both of them in 1 day unless you are really interested).
Once you have reach the top of the mountain you are about 30 minutes from Gatlinburg, TN and a must see! I would almost even skip the above just to go to Gatlinburg and Pigeon Forge, TN. http://www.eventsgatlinburg.com/
You will not regret going here. I love this place. This is where I grew up as a kid and where I got married. Its beautiful. You can ride a tram to the top of the mountain and snow ski, ice skate or shop at the mall. They make fake snow so your kids will love it. You have to include Pigeon Forge as well. http://www.mypigeonforge.com/
Pigeon Forge is at the bottom of the mountain from Gatlinburg. It is 15 minutes drive at most. It is a HUGE shopping and kids town. http://www.mypigeonforge.com/what_to_do.aspx
There are go cart tracks, tons of shopping, rides, Dollywood http://www.dollywood.com/
(kind of like Disney or Universal only country). You better plan on several days at these two places. You wont want to leave.
To reach Ashville, NC it takes me about 6.5 hrs and to Gatlinburg about 7.5-8 depending on how much we stop and how fast we drive. You can also not drive up the mountain to get there quicker.