Lots of good advice and suggestions here.
We were there in early September for a week in 2012. Stayed in the Park at the Seawall campground (no hookups) - The "A" loop is mostly tent only but we got A10 and it was great. Plenty of room and more privacy than most of the sites in the other loops. We normally boondock so the absence of amenities was not a problem.
Our favorite area was the Schoodic Peninsula section of the Park which is an hour's drive north of the main part. They've opened a new campground there since our visit and we'll probably opt to stay in it on our next trip.
We also spent a few days in White Mountain NF where another group member suggested the Sugarloaf II campground. After our stay, we'd recommend it as well. Beautiful area with lots of wildlife.