As for the Mt. Washington Hotel, we stayed there once, and not by choice, about a dozen years ago. Our daughter was in a ski race at BW that went on despite a snowstorm and we ended up marooned there. The place is ancient and our room looked it, but was adequate. The huge dining room is modeled after the great ocean liners of a century ago - think Titanic - and at that time they required men to wear a jacket, which they lent gratis to uncouth or unprepared guests like me. (I would be surprised if they still had that rule.) I loved the Gilded Age ambience of the place, which is loaded with history (Google bretton woods conference).
In the basement, the old wine cellar, hewn out of granite, had been turned into a great and unique bar. A blizzard was howling and at midnight, as I strolled around just outside, I realized why this place was the inspiration for The Shining.
It is at the center of a great XC network. I've been there since our overnight stay three times for post-race parties in the Ballroom. I don't recall what we paid for our one night, but I imagine it's pricier, probably by a lot, than most of the other suggestions.