TRI is the closest, but if you decide to fly into NC, I personally would recommend GSO. The reason is that GSO like a small town feel airport to me. I have driven there to fly quite a few times for some good fares and I liked coming in and our of there.

This is the distance, according to Mapquest: Total Est. Time: 1 hour, 58 minutes. Total Est. Distance: 106.18 miles. The route is NC 68-S to I-40 W to US 421 N.

I have also driven to CLT to fly (I am doing so this weekend, as a matter of fact), but being a hub it can be very busy. The stats for CLT are Total Est. Time: 1 hour, 54 minutes. Total Est. Distance: 95.03 miles. The suggested route is I-85 S to US 321 N.

PS. One more shameless plug for TRI--NO LINES at check in, NO LINES at security! Easy to pick up and turn in a rental car. Our two US kiosks work. DL even has kiosks and a Medallion line! The people are really nice!