Acadia National Park is wonderful, and small enough to see everything in a couple of days. Seawall Campground in the southern part of Mount Desert Island is a great, out of the way spot, close to Southwest Harbor (which is one of several nice small towns on the island). If you can, hike Mount Cadillac on a clear day (before dawn if you want to be among the first in the US to see the sun rise) and bike the carriage roads.
Hike to your heart's content; there are lots of trails appropriate for different energy levels. Across from Bar Harbor (a tiny town in the grand scheme of things, but the main hub on MDI) is Bar Island, which has some hiking trails and is accessible via sand bar at low tide. It's a fun way to spend a couple of hours without going far from restaurants and amenities; just keep an eye on the tides so you don't get stranded.
Getting out on the water would be fun too, whether by sea kayak, sailboat, or whale watching tour boat.