I would recommend looking into the town of Bethel. There's year round outdoor activities but seeing as how you'll be there in the summer it doesn't really matter. Great for families....biking and hiking tours available.
Or there's always
Moosehead Lake Maine. Definitely a good place to explore some of the state's history.
Maine offers everything from
biking,
camping,
fishing,
golfing, and
cruises. It all depends what your family is interested in doing.
How long are you planning on staying?