I grew up in Atlanta, but not being a city girl, moved to North GA and after living in 4 states, we've settled in Western NC, about an hour from Asheville. We are conservative, and I am not much of a big shopper, so I don't feel the need for the CITY life or too much culturally, but have friends and family that absolutely LOVE Asheville for those reasons. Asheville is pretty liberal, lots of sexual preferences congregate in the area - very artsy and earthy if you prefer that, but you can find conservative places as well.
One of our favorite spots around there is Black Mountain, but its a tourist town - I wanted to live there, but cost of living in that small area was too much to be realistic about raising kids there. Flat Rock is also nice, depends on what part of Asheville he would work in, how long a commute you'd want, etc.... But LOTS of sports for the kids, as well as more to choose from performing arts-wise, if you and/or your kids want to do that. I'd say, next to Atlanta, Asheville is one of the closest-to-NY experiences as far as living. And the cost of living in NC as a whole is slightly higher than our surrounding states, but NOTHING compared to NY. I have a good friend that works at Juilliard and they are always complaining about how much cheaper things are here and why they can't have the best of both worlds! :)
PS - I have a Hungarian friend that really misses her homeland, and she actually lives over the state line from us in GA, but goes to Asheville alot to meet up with other European groups of people - they really provide alot of support for those who miss Europe and have to live here in the states (she kind of feels "stuck" now, with her hubby and child, but she is VERY homesick even though they go back to Hungary for 2 months every summer and she works at an International Boarding/College Prep School). She might have some helpful advice or contacts for you, if you end up moving this way.
And hey, it's not nearly as cold here in the winter! :)
God bless you and your family as you make this difficult choice...
PS - you could probably do a good business selling the boys clothes you make - lots of people with lots of money live in Asheville and would pay good money for unique stuff like that!