The Shelburne Museum grounds are a must see in Burlington. It has 39 galleries and 25 nineteenth century structures, including a 220-foot restored steamboat, lighthouse, and covered bridge.
It's so easy to spend a whole day here. The $17.50 entrance fee for adults will even cover your return trip the next day. You might need another day to make sure you've got all the grounds covered!
On their website they list all the current exhibitions.