Michael, sounds like the Wilderness trail that runs along an old railroad bed, just outside of Lincoln, N.H. Pretty flat going for about 5 miles in, until after you cross the suspension bridge.
A better view and a slightly more difficult trail into the Pemi wilderness further up north off 302 is the ZeaCliff trail that leads into the Zealand trail. This is a popular one because it goes towards an AMC Hut.
A tougher hike is to get up to Ethan Pond, at the base of of Mt Wiley. Without snow, it's a good 1.5 hour hike straight up the side of Crawford Notch, off 302, to get to the ridge. Once you are on the ridge, the trail goes around the base of the mountain to the western side. Takes close to an hour of walking to get to the pond. There is a primitive lean to and tent platforms at the pond. The site faces west, across the pond, for some spectacular sunsets. The pond itself has some of the best flyfishing for brookies in New Hampshire.
At this time of year and the difficulty of the trail, I doubt you're find many if any folks up there. Of course, if something goes wrong, it's a tough trek in for rescuers...
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