Definitely not Stowe anymore. Vail and Airbnb ruined it. Burlington's probably not what you're looking for, either. Waterbury would be a better choice in that general area for the kind of trip you're trying to do. <= 30 mins from Burlington, Stowe, Waitsfield, Montpelier.

Woodstock definitely seems like the best pick of the three to me. Quaint town in its own right (albeit $$$), but also near Quechee (neat gorge there, very accessible) and White River Junction (good restaurants, neat downtown area).