For many, it will probably always be Saigon, the former capital of South Vietnam before the north and south were reunited in the dramatic events which ended America's military involvement in Southeast Asia.
Saigon was not a very significant city until it was captured by the French in 1859. The French made Saigon the capital of their colony of Cochinchina, and later, all of Indochina. Much of what there is to see in Ho Chi Minh City today dates from the French administration.
Naturally, many of the city's sights are also about the "American war" as it is generally referred to by the Vietnamese. There are no less than five museums dedicated to the struggle for a unified Vietnam.