If you have the time to spend 2 nights in Burlington, I highly suggest it, however the hotel market (especially near downtown and the lakefront) is usually quite pricy, especially on a holiday weekend and through leaf peeping season (September to 2nd weekend of October).
Incorporating the newly extended Ethan Allen into your trip could be a great option too. Starting July 29 the train will depart right from the Burlington waterfront. The Vermonter remains an option in Essex Junction, about 8 miles outside of town.
To connect from Boston, you can also take a Northeast Regional train to New Haven and hop on the northbound Vermonter there, or continue to New York to connect to the Ethan Allen Express. The ride north along the Hudson River is among the best views in the country. Traveling west via the Lake Shore Ltd to Springfield (to connect to the Vermonter) or Albany (to connect to the Ethan Allen) would require an overnight instead.
For a preview of what to expect in Vermont, here's a video I made in 2016 showing the Vermonter & Ethan Allen in every Vermont town the two trains traverse. I'll have to add the new towns the Ethan Allen extension goes through in a future video!