Yes, I think we have all that here.
Weather-wise we certainly do have less snow than Ithaca, but it does get cold here in the winter. I'm sure you knew that, but sometimes people move here from other parts of the country and think because we're in the South that means it's going to be like Orlando or Miami or something. It does snow here, but usually just a couple of times a winter and it's fairly erratic. We can have a year with no snow, just clear cold days below freezing and then gray rainy days where the temperature hovers around 38 and you wish it would just go a few degrees colder and turn to snow, but sometimes we can get 1-6 inches and occasionally more. We get ice storms, too, and those are no fun because they can cause power outages. Some winters are very mild. Mostly the weather in NC is pretty up and down with the exception of summer when it's hot and humid. We can have 70 degree highs in January or it can be 7 degrees for a low. In the summer it's hot—always. We're in a real heat wave right now and today is the coolest day of the week with a predicted high of 90. It's overcast and rainy looking, too. Yesterday topped 100 and the rest of the week looks to be flirting with 100s with 4 days in a row predicted to be 99. Just want you to know what you may be in for!! Also, throw in the occasional hurricane (they can come this far inland, but it's very rare), tropical storms, tornados, and plenty of good old thunderstorms, for variety.
As far as your other interests:
nature — lots of that around here. It's rolling country, but just about 2.5-4 hrs from the mountains and the beaches. NC has great beaches and great mountains with many places to explore. There are several state parks and recreational forests in close proximity to Chapel Hill and Carrboro.
kayaking (flat water) — yes, there's the Haw River and parts of the Eno River as well as Jordan Lake (big man made reservoir). In the mountains you can find a lot of white water if you want to try that.
hiking — yes, there are forests to hike in, like Duke Forest, and the Eno River State Park. There is some hiking around Jordan Lake, too, but I'd prefer the other areas and do Jordan Lake for the lake itself. Great hiking in the mountains.
living semi-rurally (my ideal is to live on a few acres with neighbors in easy walking distance and about a mile from some cool little town) — yes, there are many people who do that around here. There are lots of nicer home developments with a few acres, and then many working organic farms as well. You might check out the Saxapahaw area, or Hillsborough, or Pittsboro.
easy access to people and town/city amenities — All of the above little teeny towns are about 20 minutes from Chapel Hill/Carrboro with Sax being the furthest at about 25 minutes from Carrboro.
holistic health — yes, there are a lot of options for that here, but there are a lot of mainstream medical practices, too, with Duke and UNC both having teaching hospitals and medical schools.
attachment parenting — yes, there are many folks in the area who practice AP. We used to have an official API group, but it disbanded I think in part because it was so easy to connect with other AP-ers that it wasn't as needed as it would be in an area where other APers were harder to find.
eclectic schooling - unschooling, homeschooling, part-time schooling — There are a lot of schooling options here although I'm not aware of any part-time schooling options. They may be there, but I haven't heard of them. The traditional public schools in the Chapel Hill/Carrboro system are generally regarded as one of if not the best systems in the state. In high school in particular they can be pretty competitive as there are a lot of kids who are very academically focused as you might expect in a college town. In elementary school they offer dual language programs (Spanish and Mandarin) in several schools. The homeschooling community is very vibrant and robust here with tons of activities and programs and many chances to make connections. There are unschoolers and folks who take all kinds of approaches. There are several very good private schools in the area, as well, including a Waldorf school that goes thru high school and a Friends school. There are also charter schools in northern Chatham county (between Pittsboro and Chapel Hill) and in Saxapahaw and Durham.
spiritual evolution — I would say yes to this as well, although I am not super clued in here. I have seen mention of many spiritual offerings, though. There are couple of Zen Buddhist centers, many progressive Christian churches (and some not progressive). I'm not sure if there's a synagogue in Chapel Hill or Carrboro, but there is a strong Jewish community here and a Jewish private school in nearby Durham. Likewise I don't think there's a mosque here, but one not too far away. Chapel Hill and Carrboro are very small towns.
art (dh is an artist) — we got art out the wazoo. Everybody is an artist!
delicious restaurants, organic food, farmers markets — likewise, likewise, likewise. We've got it all out the wazoo. Bon Apetit recently named the Durham Chapel Hill area as the "foodiest small town in America". Way too much good food here!!
friendly neighbors — I've lived here a long, long time, but from what newcomers tell me it's really easy to make connections here. I think most people are pretty friendly.
playgrounds — yep, we've got 'em.
outdoor swimming (lakes, rivers, pools) — Yes, we've got those, too. See the "nature" section for the info on rivers and lakes. We have a couple of public swimming pools maintained by the city and then there are many other neighborhood pools you pay to join. There is a very active summer swim league. The neighborhood pools are really great and not exclusive or clubby or cliquey. We love ours. It's full of homeschooling, organic-eating, friendly, art-making, nature lovers.
libraries — Chapel Hill has a great library, but it is just getting ready to undergo an expansion so it will be even greater! In between it's going to have a temporary location at the mall which should be okay and the new library should be even better. I believe the Chapel Hill library is the most visited library in the state. (They keep records about all sorts of things!). Carrboro has a couple of smaller libraries, too, and there's a possible new branch of the Orange County library in the works for Carrboro. Hillsborough has the main Orange County library and it's older, but very nice, too. You can also visit the libraries on campus for more academic works.
Durham, is a bigger city than Chapel Hill, but it also offers all the things you're looking for. It generally has lower housing costs in the city than Chapel Hill which can be a little pricey. The Chapel Hill/Carrboro school district is much desired and a big selling point with real estate. If you're committed to homeschooling all the way through that might not matter to you, but I know a lot of folks who live out in the county who are looking at private school options now that their kids are school age when if they were in town they would probably send their kids to the CH/C schools. It's not that the county schools are that bad (actually I think they're probably pretty good), but that the CHC schools are that good that they're competitive with most of the private schools in the area. I know a few folks who have moved back into town from being in the county to be able to send their kids to the CHC schools. So, Chapel Hill real estate is more expensive in part based on the schools and in part just because it's a desirable low-crime, high-arts college town.