Let's back up just a bit, to properly set the stage...
Tokyo rejected the Potsdam Declaration. U.S. planes dropped leaflets over Hiroshima on August 4 that contained the warning, "Your city will be obliterated unless your Government surrenders." The first atomic bomb was dropped on Hiroshima on August 6. Three days later, August 9, an atomic bomb was dropped on Nagasaki. The next day Japan contacted Washington to surrender.
Units of the U.S. 3rd Fleet (including the USS BOSTON CA69) and British Pacific Fleet actually entered Sagami Wan on August 27, 1945, west of Miura Hanto. Tokyo Bay is northeast of Miura Hanto. To a Sailor unfamiliar with the area, entering Sagami Wan could be easily mistaken for entering Tokyo Bay. Combine this with the passage of fifty five years and you have the opportunity for some distortion of fact.
The first Allied ships entered Tokyo Bay proper on August 28, 1945. The documented order of entry, with actual time of anchoring, is chronicled on: http://web.wt.net/~gecofact/ships.htm
It should not escape notice that the VERY FIRST Allied ship to enter Tokyo Bay following the surrender was the USS REVENGE AM110, a U.S. Navy minesweeper.
The first U.S. ship to drop anchor in Tokyo Bay that day (offshore of the Imperial Japanese Naval Base at Yokosuka) was USS SOUTHERLAND DD743, a destroyer. (Following WW II the SOUTHERLAND was designated a target ship, to be expended at an unspecified date. She was sunk in the fall of 1998. The first ship to anchor the American flag in Tokyo Bay at the end of World War II, she was the last to lower her ensign, the last of the ships that entered Tokyo Bay on August 28 to serve her country.)
The official War Diary of USS BOSTON CA69 for September 2 shows her at Berth #7 in Sagami Wan. The next day's entry shows her departing Berth #7 Sagami Wan and moving to Berth #C-73 in Tokyo Bay, anchoring at 1200 hours on September 3, 1945. The (illegal) diaries of individual BOSTON crew members (that are in the BOSTON memorabilia collection) also corroborate this.