The romantic story between Fellers and Aya was entirely fictional for the film. Fellers was married in 1925 to Dorothy Dysart who accompanied him twice on his posting the Phillipines, and she also went with him to China and Japan.
The US troops seen in the film are from the 11th Airborne Division, and from the 1st Cavalry Division. These divisions were indeed the first U.S. Army units in Tokyo and their appearance is entirely correct.
The trivia items below may give away important plot points.
Warning: Contains spoiler for Lost (2004))The movie begins and ends with Bonner Fellers (Matthew Fox) in a bamboo field. The television show "Lost" which featured Matthew Fox began and ended with Fox's character, Jack Shepard, waking up and dying in a bamboo field.