I HIGHLY recommend reading this article in the Washington Post - which is an in-depth guide of all the best places to shop & eat in Burlington, Vermont, as well as various activities to try!
https://www.washingtonpost.com/graphics/2019/lifestyle/vacation-ideas/things-to-do-in-burlington/
On a personal level, we really love Burlington's farmer's market -- and if you don't mind eating pizza twice in one trip, American Flatbread is a great pizzeria in Burlington (get the maple sausage pizza!)
We really love renting out bikes and biking along Lake Champlain's bike path -- you'll pass several lovely beaches as you bike, so you might want to plan on bringing towels & snacks to make a beach day out of it!
It's especially amazing if you go far enough on the bike path to cross over the lake and go onto the Lake Champlain Islands.
This sandy lakeside beach has a little food stand, ice cream and drinks available, along with rental kayaks and SUP paddle boards. It's a lovely place to lay out on the towel, go for a swim, or paddle around. :)
Hiking Mt. Mansfield is Coty & I's absolute favorite hike in the world-- we do this hike every year. We recommend going up the Laura Cowles trail, then going down the Sunset Ridge trail.
This is the hike that we did when we eloped in June of 2024 - we exchanged our vows right at the top.
Shelburne Farms is beautiful, overlooking the lake, and has a great selection of cheese. They've got lots of beautiful walking trails too. They also have various activities planned every weekend and kids who visit can pet the goats/cows, etc. In the fall, you can pick apples next door at Shelburne Orchards and in the late summer, you can pick peaches or sour cherries. Shelburne Farms also has a lovely restaurant you can eat at and a hotel that you can stay at.
Head to Stowe, where you can visit the Von Trapp Family Lodge (where the real life von Trapp Family from the Sound of Music moved to/lived after fleeing Austria during World War 2). The Lodge has lovely views of surrounding mountains (CUE *THE HILLS ARE ALIVE*) and nice walking paths. You can even have a pint at the von Trapp Brewery.
This is such a beautiful waterfall near Stowe, VT and a fun place to swim :)
This is really popular hike among tourists and locals. Many prefer this hike over Mansfield (but I prefer Mansfield).
Also a pretty place to swim :) Bristol Falls/Barlett Falls.
Be sure not to miss the Cold Hollow Cider Mill, home of the world's best apple cider donuts. You can also visit the nearby Cabot cheese store, where you can buy reserve/harder to find cheeses and get free samples of ALL the cheeses. (yum!!)
Nearby is also the von Trapp family lodge and the Ben & Jerry's factory
The tour of the factory is short but fun and comes with a free sample at the end. It's also fun to poke around the "flavor graveyard" and get a full sized cone of fresh ice cream :)