Any recommendations are welcomed.
I don't know much about Raleigh; it is, of course, the state capital and home to NCSU. Others will be able to give you way better info. than I can about it.
Durham is without question the most affordable and probably most diverse, both racially and economically. In the past ~10 years it has really become a vibrant and lovely small city, with a thriving downtown holding both the Durham Performing Arts Center (a number of fun shows -- not cheap. But not expensive compared to similar in larger locations) and the AAA ballpark (which is fun and can be done cheaply) and any number of good-to-great restaurants (I know, Mustachians don't eat out. But hypothetically speaking.). I'm told its farmers market is also great. It's home to a roughly 25-mile bike/foot trail, the American Tobacco Trail, that I think reasonably well connects some parts of the city and is widely used for recreation (as well as commuting). I don't use the Durham buses but my sense is they aren't great; however, there is a great free bus that links the Duke campus with downtown. There's lots of cool stuff going on at Duke that's relatively affordable, and the campus, though scattered, is lovely, with a large public garden popular for strolling, families, and picnics.
Chapel Hill is more expensive and still mostly a college town centered around UNC, though there are populations that live in it and commute to Durham or the RTP for school or work. Together with neighboring Carrboro it shares a good public school system (the efforts of the state legislature notwithstanding) that keeps house prices and property taxes relatively high. But there are plenty of decent student apartments. The downtown's been sort of vacant but seems to be revitalizing. There is a good-for-the-town's-size public bus system (also serves Carrboro) that is free to the riders (mostly centered on getting people to/from campus from about 8 a.m. to 8 p.m.). It's pretty bike- and pedestrian friendly; UNC does not have adequate parking for its workforce (never mind the students), so lots of people bike or walk (and there is a not-fully-connected-but-reasonably-extensive-greenway system). Carrboro, adjacent to Chapel Hill, is a former mill town, now arty/funky/graduate-studenty; it's less expensive than Chapel Hill (but more than Durham), and sits on the ridge of the hill, making it attractive for those who want to bike or walk to campus but to miss the hill that is Chapel Hill.
The Triangle Transit Authority has a bus system that does a good job of connecting Chapel Hill, Durham, Raleigh, and the RTP. Residential areas are getting created around RTP, but it was created as just business, and is in many ways a commuter destination (somewhere to work, not live).
There's good recreation nearby -- Eno River state park, Duke Forest, and assorted others for hiking/running/biking; Jordan Lake for boating. And it's about a 3-hour drive to the nearest beaches and mountains (in opposite directions).
Last week's snowpocalypse notwithstanding, tomorrow's predicted high temperatures are in the 60s.