Yes, it did begin in Boston...
The Old South Meeting House, located on the Freedom Trail, was where the citizens of Boston gathered for large meetings in the 1700's. The meeting house was the largest building in Boston at the time. There, large protests would take place between the Patriots and Loyalists to protest and show support for the British government.
On December 16, 1773, over 5000 people gathered at the meeting house to protest the taxation of tea. Many, led by the Sons of Liberty, wanted 3 tea ships docked in Boston harbor to return to England without unloading their tea. The governor of Boston had demanded that their cargo be unloaded. The protesters eventually left the meeting house and proceeded down to the harbor where they dumped the tea into the water. This event became known as the Boston Tea Party.
The British Parliament responded with a series of acts called the Intolerable Acts to punish the colonists. This further escalated tensions which eventually led to the American Revolution just over a year later.