Black Mountain, North Carolina
Point by point.
-Proximity/easy access to large trail network
Trails are easily accessible and plentiful. Black Mountain and neighboring Montreat sit at the feet of the Black Mountains, a range with many peaks in excess of 6,000 feet (the highest your going to find east of the Mississippi)
- Is located in/very close to mountainous terrain (with 3-5k ft peaks a plus)
See above. Mount Mitchell (the tallest mountain east of the Mississippi at 6700 ft) is within running distance of Black Mountain: a hard twenty miles.
- Has a existent running community
Definitely exists and is bolstered by neighboring communities in Brevard and Asheville. Black Mountain hosts the Black Mountain Marathon and the 40-mile Mt Mitchell Challenge each February which attracts a fairly deep talent pool.
- Within a couple hours from an airport
Asheville has a small regional airport. Charlotte-Douglas is roughly 2 hours away and can get you almost anywhere.
Bottom line: If you are interested in trail running and especially interested in serious vert on the East Coast, Black Mountain is the ticket. The Adirondacks and the White Mountains in New Hampshire could give it a run for its money, though the winters are less hospitable. Differences in culture are also fairly pronounced.