Burlington itself is a city with no more (or fewer) trees than most other cities, though the view out over the lake from the top of Main Street can be stunning at sunset and there are beautiful trees in Lakeview Cemetery a mile or two north of downtown. (I have a family member there.) If you're into running or walking, the Island Line rail-trail crosses the bottom of College Street; head north (turn right so the lake is on your left) rather than south unless you like railroad yards.

That said, it's the easiest place in Vermont to fly into, there's nothing wrong with it as a base for driving around, it has good shops/restaurants, and walking around Church St. Mall (a pedestrian street, not an enclosed shopping mall) in the evening is fun if the weather cooperates. Head east (nominally south) on I-89, get off at Exit 10, stop at Ben and Jerry's because everyone does, and continue on to Mt. Mansfield. Or, there are a bazillion other places to get off the highway. It's hard to go wrong with foliage in Vermont as long as your timing is right.