Chris, I think the only legal campsite near the Percy area is on the Cohos Trail -- Percy Loop site, on the north face of N Percy, not too near a road.
Check out this information on where to camp from the Cohos Trail website. Make sure to verify before you go. Some of their shelters are closed this season due to logging operations, but I think they are all further north. Neverthless, the CT is still developing so you can expect accommodations to fluctuate.
If you're doing the Percy Peaks, that's one great hike in your future!
Chris, another option is Jericho Lake in Berlin off of rt 110. No services but its a lot closer. One caveat is that there is a party crowd on occasion, so I would not leave gear unattended.
You could also try the Milan Hill State Park on 110B just a few miles east of Percy. (The website lists it as 116, but they've confused it with Weeks State Park, I guess.) I ended up there by chance one very rainy weekday night in August and just slept under the picnic-gazebo roof. Restrooms were open. No one else was there. No Iron Ranger and no one showed up to ask for money. . . . I went back onto the Cohos Trail the next morning thinking that I should go back to this place sometime to see the great view it is supposed to have but haven't revisited yet.
I am tentatively planning a trip to the North Country and am zeroing in on staying at Maidstone State Park CG across the river in VT as a base. Anyone ever stay there and have any opinions pro or con?