The number one trail I recommend is the Hamster! A bit on pavement on this route, yet at least byways! I especially like the run Errol to Pittsburg! South of Errol (north out of the Jericho area) I vary from the Hampster and I haven't run that portion as of yet and if you do, please let me know what you think.
Near Berlin NH I like staying over in Evans Notch. It's another part of the White Mountain NF and much less traffic. Some free spots but rater hard to get one and the NF sites are cheap enough and well maintained. If you include Mt Washington in this run, go for Barnes Field vs. Dolly Copp proper. They paved paradise at Dolly Copp proper! The Field is still cool!
Another route is to follow the NEBDR
North East Backcountry Discovery Route (NEBDR) Map & Information I linked their website so you can see it goes a whole lot further than just NE! I used then as a guide to explore along the Blue Ridge Mountains last year!
The NEBDR mixes pavement to single track, so some areas (especially southern) you may need to route around.
Gotta run, but ill get back to this!