Backcountry camping is allowed off of many hiking trails along the Kancamagus highway in the White Mountain National Forest.
There are different rules for different areas of the forest, be sure to read and understand all Rules for Back-Country Camping on The Kancamagus and read all information posted at the trailhead before you head out. It is also a good idea to get current conditions for the area you plan on hiking before you go as there is normally no cell service on the trails near the Kancamagus.
Backcountry camping is basically all over the White Mountain National Forest, but there are some areas that can be more populated, like Sawyer Pond. There are campsites there, fire pits, platforms, and a bathroom, being on the pond also makes it a popular spot for hikers and campers.