Castle Island is one of the Boston Harbor Islands that is not exactly an island anymore -- it sticks out into the harbor but is connected to a residential part of South Boston. It is home to Fort Independence, built in the early eighteenth century and used in the War of 1812. The fort is open some weekends in summer for tours.
Wide paths with benches and grassy knolls make it great for walking, jogging, or relaxing by the shore. When the wind blows from the northeast, it is also a prime spot to watch planes land at Logan Airport just across the harbor. Take the T Silver Line from South Station to City Point.