While you are in Burke, drive up Rt 5 to Lake Willoughby. If you want to go for a hike there is a trail on the east side. You can go to the top of Mt. Pisgah, you can keep going north on the trail and come back out onto Rt 5 but you'll have to walk the ~2.5 miles back to the south entrance. Otherwise you can turn around and go back out the south entrance but do go somewhat north past the top, there are great views of the lake from a few lookouts.