For kids, FUEGO (a member here) may have more input. I have none so my opinion is probably not useful.
Hey Hatcher! I'm in Raleigh with 3 young kids (oldest 2 are 8 and almost 10).
COL is a lot lower here for some things, especially real estate. My wife's company relocated a couple thousand people to Raleigh from NYC. One of her relocated coworkers cashed out $500k or so in equity from their crappy townhouse in Brooklyn and bought a 5 BR 4000 sf McMansion and furnished it with the money left over. His family came down to visit and thought he won the lottery (I take it houses like that aren't $400-450k in NYC). Overall people liked the move down here, except for a few that grumble about the lack of transit (though they don't complain about all the free parking almost everywhere).
We are in Wake County schools. Overall, there aren't any bad schools in the district, just great, good and less good. The worst performing schools don't do well because of challenging populations, but that doesn't mean the teachers aren't good or that your kid can't do well there. We happen to be in one of those poor performing schools (lots of ESL kids, 80%+ poverty) but our kids maintain top grades and test scores. It also means they have a dedicated AIG (academically and intellectually gifted) teacher for near-solo instruction. Class sizes are small (between 12 and 18 kids most years, 21 kids is the largest class they have ever had). We are happy with the school, however on paper the stats don't look pretty. But we have plenty of options to transfer if we grow unhappy.
Most schools score very well, especially if you end up in the wealthier suburbs like Wake Forest, Apex, and Cary. Magnet schools are plentiful, which means you can send your kid to a variety of schools that have different themes and focuses. Engineering schools, health sciences, early college, advanced academics, foreign language immersion (Chinese or Spanish IIRC). International Baccalaureate programs starting in elementary school, broadly available AP courses in high schools.
And hey, public schools are free.
Real estate taxes are generally a lot lower. We pay about 1% of the house value, and you can find 3-4 BR houses in the $150-300k range pretty easy. More if you want to live in an exclusive area obviously. So imagine $1500-3,000 property taxes per year.
Unions don't exist here, so services are generally rather inexpensive. I just had the siding and windows replaced plus some major roof repairs and the price tag was $9k. YMMV of course.
Based on what friends tell me, social life is a lot cheaper in Raleigh. I think $3-4 is a lot to pay for a beer but my Raleigh friends that moved to NYC come back to visit and think $3-4 is happy hour pricing.
It really depends on what you spend money on now. I also have friends here that barely scrape by on $200-300k household incomes. Custom build a house or a lakehouse, buy some luxury cars, sign your kids up for travel sports, get a boat, and you, too, can struggle to get by on $200-300k even in Raleigh.
As far as culture, probably half the residents of Raleigh aren't from Raleigh. Lots from PA NJ NYC MA area. The city leans slightly blue while the more rural areas around Raleigh lean red. The triangle area is home to 3 major research universities, so tons of college grads and PhDs are floating around (I saw somewhere that we have one of the most educated populations).
Downsides are hot, humid summers during July and August (not entirely dissimilar to NYC in my experience). Rural/urban political strife (NYC vs upstate?). Lack of transit if that's your thing. Traffic in certain areas during rush hour if you have a long commute.
Needless to say, I love Raleigh. So maybe I'm biased. I think our roads have room for one or two more cars if you want to come on down and join us.