It can be cold and even snow in Tennessee during the winter months.

I DO NOT recommend and RV. Have you done this before?
You will not save money. If camping is your thing then this might be ok.

Tennessee--
Memphis
see Elvis/Graceland
Great places to eat at
Gus's Fried Chicken--inexpensive
Blues City Cafe
Rendevouz
Brunch at The Peabody-expensive

Nashville-
don't miss The Loveless Cafe
Pastaletos(might be spelled wrong)=best popsicles ever
See County Music Hall of Fame, maybe Grand Ole Opry
See The Hermitage House

Smoky Mountain National Park
Gatlinburg/Pigeon Forge/Dollywood

Florida
Disney-include a waterpark there too
Keyes, Everglades
Nasa
Maybe Seaworld


I'll let other comment on Georgia and Alabama. Have been thru each several times, but nothing there is a real standout that would make me want to come from a foreign country to see.

How many days/weeks in Jan/Feb? If you want to arrive and depart from the same airport, I would suggest Atlanta.
Depending on the weather conditions at the time, decide if you are headed for Florida or eastern Tennessee first.
You can come south from Chattanooga to see northern Alabama.
Consider riding the Amtrak Crescent from Atlanta to New Orleans and spending a night there before taking the City of New Orleans north to Memphis. You shouldn't need a rental vehicle there. You can do better by booking cheap hotel rooms on Priceline instead of using a rental camper.

Hi all

We do al lot of camping in South Africa and have an RV. We camped in the US during 2009. But putting up tents with little ones is something I do not want to do. Why would you recommend camping above an RV? We enjoy wildlife more than anything else and want to stay in nature...

We want to fly in on Jan 1st and travel for about 6-8weeks... we want to have a relaxed pace so that the kids don't have to be travelling in a car all day long.

A friend of ours have a camper we can use, so that excludes the costs... any other reason we should rather book a hotel room? Is it too cold to stay in a RV?

Having the free use of an RV might make it cheaper than motels.
You have to consider the cost of fuel and campsites with electric hookup. The campsites that are open can be scarce in Jan-Feb. The Great Smokey Mtns. NP in eastern Tennessee will likely have snow. http://www.nps.gov/grsm/planyourvisit/weather.htm
Are you looking for coastal or mountains? Elevations above 5000' are quite likely to have snow. If the RV's heat is made by propane, be sure the unit has a Carbon Monoxide detector with a new battery.

Our kids are living on a farm and staying in hotels will just make us all go mad. We would like to see the warmest areas during this trip and we are not worried about big cities as we enjoy nature more. We have friends living in Tennessee, and we will stay with them there. Should we come to a place that is too cold for staying in an RV, we really do not mind staying in a hotel for a few nights before moving on.

Which states have reasonable weather during this time?

Like tomfuller stated, anything with an elevation above 5000' might have snow. The coastal areas will not have the same risk.

In the Charleston area the Francis Marion National Forest, and Frances Biedler Forest are both pleasant natural places.