I'd suggest Stowe (Mt Mansfield), one of the better places in New England. Excellent choice of trail types (for New England, at least), very likely to have some of the best conditions in N.E., and a very pleasant and welcoming town. Less than 1 hour drive on decent roads to Stowe from BTV (Burlington), and UA has several flgihts/day IAD-BTV.

Many more choices if you fly into MHT (Manchester), though none as good as Stowe. Several of day-trip areas (Gunstock, Sunapee, etc) within 45 mins drive, and several destination-type places (Waterville, Bretton Woods) about an hour from MHT. None of them beats Stowe, though.

1/4 would be a great time to go -- relatively few people joining you, as it's between the Christmas break and MLK weekend.