There are tons of hotels near Burlington and in burlington. Shelburne as you go into burlington and there is also Essex Junction (maybe a little cheaper since it is next to it but not in it). Just google the area or your favorite kind of hotel (comfort suites, holiday inns, etc.). I am with the other poster, go to Shelburne museum (so cool, bring picnic lunch too), there is an aquarium near Lk Champlain waterfront as well as rides on the lake on big boats (with lunch if you like), Chocolates (I think its Lake Champlain Chocolates) factory.
Have fun, I go to my dad's in Stowe plus I have lived on Lake Champlain and in Underhill now I am in the sticks of PA!