On what hill did the Battle of Bunker Hill take place?

The Battle of Bunker Hill was fought on June 17, 1775, during the Siege of Boston in the early stages of the American Revolutionary War. The battle is named after Bunker Hill in Charlestown, Massachusetts, which was peripherally involved in the battle. It was the original objective of both the colonial and British troops, though the majority of combat took place on the adjacent hill which later became known as Breed's Hill.

Much has been written in the wake of this battle over how it was conducted. Both sides made strategic and tactical missteps which could have altered the outcome of the battle. While hindsight often gives a biased view, some things seem to be apparent after the battle that might reasonably have been within the reach of the command of the day.