From North Conway: 3.5 hours.
I love this town. No really, I do. It's the home of the University of Vermont and it's the largest town in Vermont... however it's still not huge. It sits on the banks of Lake Champlain and has a very homey, artsy, warm feel to it.
Big recommendation: You MUST go to the Church Street Marketplace. It's a sweet little pedestrian area with shopping, food, and sidewalk artists, all in front of a big beautiful church.
http://www.churchstmarketplace.com/Other ideas: On your way to Burlington, you'll most likely pass through Montpelier, Vermont's capital. Take a few moments to check out their capital building, as well as Main Street Grill, a restaurant by the New England Culinary Institute. You'll get an excellent lunch prepared by the next generation of top-notch chefs.
Interesting fact about Montpelier... Although it IS the capital of Vermont, the reason it is so tiny is because it lies in a flood plain. It is not uncommon for buildings to wash out during heavy precipitation seasons.