14 mile trail that runs along the Burlington waterfront and extends ~3 miles out into Lake Champlain on a narrow path (the Colchester Causeway); awesome place to run, walk, or bike, and the Causeway is truly gorgeous (pro tip: check with your hotel about bike rentals, sometimes they have them for free!)
Vermont is known for great hiking, and Mount Mansfield (the tallest mountain in VT) is a quick drive from Burlington (this trailhead is ~40 minutes from downtown); from the top you get spectacular sweeping views of the Green Mountains and can look down on Stowe Resort. While you certainly don't have to pick this trail, getting out into nature is one of the best parts of Vermont!