Montpelier or Waterbury if you want to be on the I-89 corridor with easy runs to Stowe, Burlington and Barre. Waitsfield or Warren if you are here to ski or to spend time in the Mad River Valley, which is beautiful but a good half hour off the interstate.
Yes. Amtrak's Vermonter stops daily at Waterbury and at Montpelier Junction, with through service to New York and Washington. It is a genuinely pleasant way to arrive, but you will need a car or a lift once you are here, especially for the valley.
Mad River Glen is small, steep, cooperatively owned, largely ungroomed and does not allow snowboards. Sugarbush is much bigger, split across two mountain areas, with more grooming, more lifts and more lodging at the base. Locals often buy passes for one and visit the other.
A single night covers the town itself comfortably, but it works well as a central base for several days. Stowe, Barre, Waterbury and the Mad River Valley are all within thirty to forty minutes, and Burlington is under an hour.
Live prices for every hotel and inn in the area — free cancellation, updated daily.