I checked Frommer's Burlington section. It only lists a few things: The Ethan Allen house, Lake Champlain, the Shelburn and the Robert Hull Fleming. On a search on my own, I found Echo Lake Aquarium, Waterfront Park, Church Street Market Place, Lake Champlain Chocolate Factory and the Burlington Earth Clock.
We'll be there for 5 days with two kids under 12 years old. We'll be going to the beach probably every day. What are the best beaches? We'll try to go to all of the above landmarks, but is there an amusement park (no matter how small) for children in the area? Is there anything else we should see that I didn't list?