Yes we have airplanes in NC
The first homebuilt ever, was flown in North Carolina (December 14, 1903, Kitty Hawk, NC.)
There is plenty of GA and EAA aviation in the Raleigh area. Hangers and cost of living?
As far as hangers, the situation actaully is surprisingly not that good, in part due to RDU tearing down the GA hangers adn Chapel Hill closing. It will be tough to impossible to get a hanger at or close to KRDU. There just are not that many airports with hangers or hangers available near RDU. There are airports close by, some small private and fly-in home type airports (Cox, Eagle Landing, Deck Airpark NC 11, Fuguay/Angier Field 78NC ) with a few hangers but none to rent. Expect a 30-45 minute drive to the nearest airports with readily available hangers (Stanford, Johnston County, Siler City). Readily might mean a wait list.
Hear are the two closest EAA chapters:
http://www.eaa1114.org/pages/home/index.php (Cary/Apex, Cox Field)
http://www.airnav.com/airport/NC81
(meets at private field NC81, cox field, no hangers)
http://www.blueasp.com/506/index.html (Smithfield, Johnston County Airport)
http://www.airnav.com/airport/KJNX
(32 sm from RDU, direct)
The most likely place to hanger is: (27 sm from RDU, direct)
Sanford-Lee County Regional Airport
Sanford, North Carolina, USA
http://www.airnav.com/airport/KTTA
Sanford is a new airport (moved from old location 5 years ago) and hangers are new at about $225 month. This airport is a solid 35-45 minute drive from RDU airport. They have a wait list but they build new hangers from time to time.
In General Raleigh NC and surrounding areas is very expensive area to live, so buy where you can. Like most places the further out you go the better. Apex use to be far out and housing was cheap, but that is changing. There is sales, income, property and personal property tax (car, boat and yes tax on your kit plane). I have not owned a plane in this state so I can't tell you the tax rate. If you are working in the RTP (research triangle park) than there are plenty of appartments to rent, which I would suggest until you figure out what you want.
Here are two other airports that might work?
5W5 Triple W Airport (18sm to RDU)
Raleigh, North Carolina, USA
http://www.airnav.com/airport/5W5
(There are some hangers but they are in bad shape and hard to get.)
5W8 Siler City Municipal Airport (40sm RDU)
Siler City, North Carolina, USA
http://www.airnav.com/airport/5W8
(I know they have new hangers there, but this was a few years ago. Not sure of the availability at this time. I know they plan on building new ones)
Airports you can't use any more:
KRDU is a busy airport served by almost every major and regional airline. The GA fleet has been run off with the demolition of the old metal T hangers. They are building new hangers of the large corporate type. The new Sanford airport above was built in the last 5 years to serve GA and make up for the loss of GA hangers at RDU. RDU does have tie downs. My guess is a hanger will be insanely expensive if you could even get it. RDU is 10 minutes from my house.
IGX, Williams Chapel Hill is owned by the University and has closed to GA aircraft for the most part; You can't base a plane there. Again Stanford-Lee was made to also take this loss.
http://www.airnav.com/airport/KIGX
There are airports North and North East of Raleigh which I am not familure with because I live south south-west of Raleigh, but they are also 40-1:20 drive time from RDU. Welcome to the area. I was a little surprised at first but Stanford is 25 minutes from my house and the airport is new, 6500x100 runway long enough to land a B737, so I can't whine too much. I would love to get a hanger home, but think I will do that in Florida.
Good Luck George