In the White Mountains, a northern section of the Appalachians, sits South Moat Mountain. This hike is not far from Conway, NH.
I went up in winter, so you may want to be prepared with snowshoes or winter traction for your feet. See if you can get an update on the recent trail conditions. Wool or a synthetic fabric that wicks moisture are good clothing options for the cold of a summit in New England in January.
It was dark and overcast for a bit, but there were still nice views of the mountain ridges nearby. If you wanted to extend the day you could continue on to North Moat. That would add a few more miles to your journey.
The hike is an up and back of about 5 miles. You can park by the southern end of the Moat Mountain Trailhead and take it all the way up. View a map of the trail. Have fun!