Chapel Hill is a nice place to live, like bjo said, 9 months out of the year. The problem is with those 3 months of the year when you wake up to go outside, and just after sunrise it's already 80 degrees and foggy. It's never fun when you start sweating first thing in the morning
As for skiing, your best bet would be to head to WV. It's probably actually cheaper too, even with the extra 1.5 top 2 hours of extra driving you have to do. Most of the NC ski areas are located in Boone, 4 in all, and every hotel in that city overcharges by about 200%. As far as the ski areas go, most of them will be filled with beginners who turn the easy trails into war zones with all the injuries, and the occasional local racer using the downed skiers as slalom gates. Silver Creek, the sister resort of Snowshoe is probably the least crowded of any eastern resort. It's about 3 miles down the road from Snowshoe, and they can be skied on the same lift ticket.
If you want to see some really strange mountains, you can check out our Monadnocks in the Western Piedmont. They formed by erosion, and not uplift. Pilot, King's, Stone, Uhwaries, Hanging Rock are just a few of these. Probably one of the least crowded places in the state are the South Mountains, a section of the Apps that are separated from the main portion of the Appalachian chain. Believe it or not, out mountains are also high enough to receive snow into May.
As far as North Carolina goes, there are lots of golf courses. Down in Southern Pines and Myrtle Beach, they have some of the highest concentration of Golf Courses in the country. Even the lower end ones are just as nice as the 2 private courses we have at my part time job. They have to be nice to be competitive. We actually have some very good mountain biking (there are some real nice greenway trails that run right through CH), and an amazing parkway in the mountains that in the spring and fall can match up with any view out west.
The beaches here.... Well, they suck
Too many gaudy colored condos and chain marts for my taste, but there are a few last bastions of real beaches. Try Bear Island for one.
One last thing about CH, due to our airports lack of a major hub, and it's central location between just about all major airlines major hubs makes planes tickets incredibly cheap here. Tickets to Denver, Salt lake, Reno, Sacramento, Seattle can be had for as little as $150, and rarely go over $200 by too much.
Oh yea, one more thing, people tend to wear this disgusting, makes me want to puck, tarhole blue color around there