My favorite times for the DC area are April and October. Not too hot, not to cold. Either spring is coming on full force or the leaves are changing - the most beautiful times of the year in DC. By October, people have mellowed out from the summer tourist season, most of the mosquitoes are gone, the night air is crisp. In April, people are getting excited about summer on its way, the flowers are blooming, warm days aren't yet humid enough to swim in.
Traveling down the Appalachians following fall is pretty amazing. Shenandoah National Park, the Blue Ridge Parkway, Great Smoky Mountains National Park: all are not to be missed.