The Pitcher Inn, about an hour south of Burlington, in picturesque Warren, Vermont, is a fabulous place with an outstanding restaurant (and great breakfasts that only are available to guests of the inn). I would opt for the Pitcher Inn over Shelburne Farms if you don't object to the distance from Burlington. There is great hiking and other activities nearby at Sugarbush Resort. Also, if you go make sure to check out the Vermont Country Store across the street.