Two places come to mind, on the MA/NH border and about 30 minutes from southern ME attractions is
Salisbury Beach State Park Walk to the beach from your campsite! Plenty boating, fishing, biking with one beach on the Atlantic and one beach on the Merrimack River.
In RI there's
Fishermens State Park You have the Historic Newport Mansions, short drive to several beaches, fishing and lot & lots of biking. You can ride your bikes from your campsite to the block Island ferry and bike scenic Block Island, makes a great day! :C
Both campgrounds have loads of seafood restaurants in the areas which includes Block Island!
Also from Fishermans you can do a day trip to Mystic Seaport.
Hope this helps
Mike