The peninsula was the site of the Battle of Bunker Hill (which was sometimes called the 'Battle of Charlestown', since the fighting did span across more than one hill). This is also where Paul Revere started his well-known Midnight Ride, which I still think sounds more like something you'd do with a lady.
As to the town of Charlestown - well, while it was established prior to 1775, little of it survived the Battle of Bunker Hill. Continental Army snipers were stationed here to harass British troops, and the British set fire to the town to root them out. Most of the buildings were razed, and the rest was burned during a raid in January, 1776. The only part of the town to survive the war was the street layout.
Charlestown was rebuilt, however - it's now a part of Boston.