Could it be Summerville where your neighbors are moving? It is a suburb of Charleston and a very beautiful town but growing rapidly.
Charleston and Charlotte are good sized cities with the usual urban issues. Both have outstanding areas around but bear in mind those metropolitan areas are the most expensive in both states.
Charlotte and the surrounding areas do have cold winters, not as much as you have now but they do get ice storms and the occasional snow. From the midlands of SC down to the Lowcountry along the coast you will have mild winters.