I'd like spend two/three nights out near Mt Washington at a single base camp. Is it possible to set up a base camp, hike Mt Washington and some surrounding ranges from that camp? Any recommendations on camp sites that are within range of summitting Washington, but convenient for other Mts/Ranges as well?
Ditto on the Great Gulf. Or, hike up to one of the RMC huts and set up there. You can easily hike combinations of Madison, Adams, Jefferson and, on a long day, Washington from Crag Camp or Gray Knob. And, you don't lose all the elevation returning to base.
I would say setting up camp in the Great Gulf would be your best bet as it is a central location for the Presidential Range. You can easily hit the Northern Presis one day and Washington the next without having to trek very far. There are at least 5 different established campsites along the Great Gulf Trail ranging from about 2,200 to 3,500 feet.