Moose Point State Park is a small coastal state park located in Searsport. There are around two miles of trails in the park but the primary attraction is the beautiful waterfront setting. I visited the park today and hiked 1.4 miles around the perimeter of the park enjoying the views of Penobscot Bay. The park closes for the season at the beginning of October but they allow visitors year round (although park facilities are closed and the entrance road is gated.) The park also has a small beach, playground and picnic area, and gazebo and group shelter for events.
Here is a map of my hike.