Fly to Asheville through Charlotte or Atlanta

I would certainly fly, you would waste a good amount of time driving. Also, I would fly into CLT & rent a car there. You can drive to the Mts. & be there, while waiting for a connection to Asheville. If you are price conscious, I also wouldn't rule out Greenville, SC (GSP) to fly into. Southwest services it I believe, & it is only about 75 miles away (From Asheville).

It takes 3 hours and 40 minutes both through Atlanta on Delta and Charlotte on USAirways TO Asheville.

If you are going to use Southwest you are going to have to drive to Fort Lauderdale and fly from there. And you will have to change somewhere like Memphis or Baltimore...so I would forget that one.

I would fly to Charleston, for a few days (you don't say you've really been there).
Drive up the coast to Wilmington, across the state through Winston (Old Salem) to Charlotte. Go up to Boone/Blowing Rock and drive down to Ashville on the Blue Ridge Parkway. Back to Charleston.
Or make a loop beginning and ending in Charlotte or another town with a low cost airline. Could even be Raleigh.
BUT I would give Charleston another look. It is only about 3 hours from Charlotte.

You can fly JetBlue from Ft. Lauderdale into Raleigh-Durham. That puts you two hours from the beach at Wilmington and three to five hours from the mountains. Plus you can visit Old Salem on the way to the mountains, and there are a few things to do in the Triangle as well.

On the other hand, if you drive up you can visit Savannah, Charleston, Beaufort and the islands, but you wouldn't have time for the mountains as well.

When are you thinking of doing this? You can get a good rate at http://www.thesurfsuites.com/ through the end of February.

The OP says they have already been all the way to Myrtle Beach.