I see both sides - fly to focus on the mission and drive as a test trip. You definitely want to visit in the summer before moving. There is a huge difference in Asheville and Wilmington, climate wise but I could probably retire in either place and be happy. I grew up in Louisiana and lived in NC for two years and there is a big difference in NC and the Gulf Coast. The NC Coast is definitely hot and sticky but it is really only bad in July/August. Nice extended spring and fall. I would even camp in the summer but I would want a shady site. YMMV - after dealing with Louisiana heat and humidity for 35 years, almost every else I've lived has been more tolerable in the summer so I have a different scale from someone who lived in say San Diego his or her whole life.
From your list, Charlotte is attractive because of it's proximity to the coast and mountains, not to mention it's a nice city from my limited visits. Ditto for Raleigh, though that's not on your list.
One odd hobby you could pick up in NC is collecting shark tooth fossils on the beach. The place I know is on Camp Lejeune but I'm sure there are other places along the coast.
Have fun and congrats on retirement!
