The American Revolution began in Philadelphia, Pennsylvania, with the Declaration of Independence.
On the ground, major battles took place along the East coast of what was to become the United States (back in the 1770s, there were only 13 colonies that took up what are now Maine, New Hampshire, Vermont, Massachusetts, Rhode Island, Connecticut, New York, New Jersey, Pennsylvania, Maryland, Delaware, Virginia, the Carolinas, and Georgia). Much of the action happened in what is now New England, New York, and New Jersey, though significant battles also happened in the south, as well.
There were also a few naval engagements along the coastline of the U.S., though these usually involved private boats owned by revolting U.S. citizens (privateers). After all, the British had the largest navy in the world at that time, so there was little sense for the Americans to challenge them on the water. However, numerous American vessels were captured by the British in the Atlantic Ocean, especially in the early days of the war.