Asheville wouldn't work as a day trip, but with places like the Biltmore Estate (will take most of the day if you visit there, but it's worth it), Grove Park Inn, etc.. and a host of outstanding restaurants (Nightbell, Curate, the Admiral, Laughing Seed Cafe (vegetarian), among others...) and a bunch of breweries, it would have something for both of you. It is about 4 hours from Mt. Pleasant so you could probably drive to Asheville 1 morning, spend the day at Biltmore then hit a nice restaurant, hit a brewery or two, then head to a downtown bar to listen to some music, stay overnight, then spend the day in downtown Asheville, which has a vibrant arts culture, have lunch and head back. My wife and I try to get there for at least a night or two every year.
I've only been to Charleston a couple times so can't really comment on that other than to say it definitely has both of what you are looking for, both historical and outstanding restaurants.
Raleigh and Durham have some outstanding restaurants with nationally renowned Chef's. Ashley Christensen just recently won the James Beard Award for Outstanding Chef in the country and she has multiple restaurants in downtown Raleigh: Poole's Diner, Death & Taxes, Beasley's Chicken and Honey, Chuck's (burgers), Fox Liquor Bar, Poole Side Pies (Pizza). Two other place you might want to try in Raleigh include Brewery Bhavana (a Dim Sum restaurant co-located with a brewery, a flower shop and a book store) which has also received national recognition multiple times. Seems like an odd combination, but it works. Only caution is that it's loud in there. The other is Bida Manda, a Loatian based restuarant, which is right next to Brewery Bhavana and has the same owner. If you want to go there though, you need to book now as it's hard to get reservations there, unless you want to eat really early or really late, Friday and Saturday are the worst. A friend of mine recommended the Stanbury, but I've yet to try it out. The "Pit" in Raleigh is one of the more famous BBQ places, and while good, I thought it was kind of pricey. I won't try to recommend a BBQ place though, as you will find that opinion's vary greatly on this board, but there are a bunch of very good ones all over both states so ask the locals where-ever you are at the time.
Morgan Street Food Hall just opened recently in Raleigh and has a bunch of different offerings, although I've yet to get there.
Someone like
@garnetpalmetto can probably give advice on Durham restaurants as I don't know them as well.
If you haven't read the first post in this thread, I'd recommend it as GP put a lot of information on places to go, things to see, etc...