The Second USS Boston: This was the second warship named Boston, a seaworthy 24-gun frigate, built by Stephen and Ralph Cross of Newburyport, Massachusetts for the newly created Continental Navy. She was commissioned in 1777 under the command of Captain H. McNeil.
USS Boston (1776) is most notably known as the ship that in 1778, under the command of Captain Samuel Tucker, sailed John Adams and his son John Quincy Adams (both future presidents of the United States) across the Atlantic from Massachusetts to France. It was a treacherous journey, with winds blowing them off course and lightning splitting a mast, causing multiple casualties. At one point guns were fired when giving chase to the British merchant ship Martha. According to John Adams’ diary, the confrontation ended with prisoners being taken and the payload being transferred to USS Boston. Adams also writes that Martha’s captain was very much a gentleman.
As Diplomat to France, John Adams joined this voyage with the intent to meet up with Benjamin Franklin and secure France as an ally. It was an endeavor that was already successfully moving forward as the Treaty of Alliance with France had been signed before his arrival. Still, there was much more to be done.
In her career with the Continental Navy, USS Boston captured a number of British vessels during the American War of Independence. Ultimately captured herself by the British in 1780, she then served them as HMS Charlestown during the remainder of the war. After the war she was sold for breaking, most likely to a yard in Great Britain.

In this painting by James A Flood frigate USS Boston is depicted maneuvering her way to sea, on a broad reach with the wind on her port quarter. She is on the Cooper River, a little upriver from the city of Charleston, South Carolina, partially visible in the distant left.

Please note that USS Boston is a popular term only;  technically speaking, American Colonial and United States ships of war did not carry the prefix USS until 1907.

Connect to a brilliant portrayal of John Quincy Adams, including his association with USS Boston, written by Howard Dorre in his blog:  Plodding through the Presidents

USS Bostons Link: USS Boston Shipmates