I did a Vermont bike trip 4 years ago with Adventure Cycling Organization and it started in Burlington. What a cool college town, right on the shores of Lake Champlain!
Here's a link to the trip I took. Cycle Vermont
I do remember a couple of nice bike shops there and lots of nice little restaurants. There is a walking/pedestrian area in the main part of the downtown and it is nice to stroll around and see all the people and hit the bars and grab some food. Since it is a college town it is unique and bohemian at times. It takes about 5 minutes to get out in the country on the North side of town and you are in some great riding. There is also a bike path system along the lake front. It is a good sized city though and lots of traffic in town and a couple strip malls areas with lots of hotels, etc. I do remember a large Eastern Mountain Sports store that also has lots of outdoors clothes and supplies (like REI but not as good). But that is on the outskirts of town.
Have a nice trip. I'm jealous Here's a few more links.
Of course I don't know how long you will be able to tour in Vermont but I would definitely try and ride as much of Route 100 as I could. It is narrow, winding, hilly, and FUN! When I do my tour this summer I will make sure I do as much of route 100 as I can.