Not trying to cover everything but for starters:
For Vermont, you could stay in Burlington (Hilton, DT, and HI) and drive to Stowe for Stowe, Sherbourne for Killington, Waitsfield for Mad River Glen, Warren for Sugarbush, and others.
New Hampshire: North Conway has a HI with a number of areas close.
In New York you could stay somewhere like Saratoga Springs and drive to a number of areas.