North Carolina has a lot to offer.
FWIW, I’m a transplant from Western NY State, but have lived here for more than 30 years, in Cary, a bedroom community of Raleigh, the state Capital.
Suggestions for Asheville are spot on! Wonderful area!
Raleigh has a really nice science museum, NC Museum of Natural Sciences, and a couple other museums; History (also in downtown) and NC Museum of Art (slightly out of downtown on Blue Ridge Road.
Durham has the Museum of Life and Science, the Nasher Art Museum at Duke Univ., and a Tuba museum.
Nearby in Asheboro (very close to the center of the state) is the NC Zoo; very highly rated! It’s over 500 acres.
Back in the mountains is the Blue Ridge Parkway (which may give you trouble during end of Febr.- early March).
In Greensboro is the International Civil Rights Museum; Greensboro was the site of a sit-in at the Woolworth’s lunch counter in the 1960.
Down at the coast (but think first, it’s a lonnnng coast!!) you have Kitty Hawk, Cape Hatteras, the NC Aquarium and Fort Fisher.
The craft brewery scene is all over the state; so is wine. A couple falls ago my wife & I did a lot of wineries in the Yadkin Valley area, just west of Winston-Salem. Also down east in Duplin County, and others. Good stuff, all over.
New Bern (pronounced NewBern locally)(and Durham sounds much more like Durmm than Dur-ham) has Tryon Palace, a reproduction of Governor Tryon’s Palace when NC was a colony.