I'm partial to Washington, but I may be a little biased.
It does look inland on the map, but the Pamlico River is wide and offers great sailing as far west as Washington. I think you'd find the area to be a great cruising ground for your 25-footer and a fun place to sail the Scot, as well.
There are lots of secluded creeks and bays that make great overnight anchorages, as well as maritime-oriented places to visit that are all within easy cruising range. A long day's trip will put you in Ocracoke or Beaufort, or you can anchor overnight and break it into two days. From Beaufort, it's easy to get out to Cape Lookout Bight, an incredible spot to visit.
It is pretty hot for a couple months - mid July through August, especially - but we have a nice long sailing season and the winters are pretty mild. We might get one or two very light snowfalls each winter, rarely enough to stick on the ground, and some winters none at all. Most people keep their boats in the slip year-round, as the river doesn't freeze over.
I'm not too familiar with the drive to D.C., and I'm sure it's a pretty good haul, but it would be at least a little shorter from Washington than from New Bern or Beaufort/Morehead. The drive to Raleigh is also considerably quicker than it used to be thanks to bypasses around Greenville and Wilson; we can be in Raleigh in about 2 hours.
Let me know if you have any specific questions or if there's anything I can help you with.