Rambo described it as a "small place". This is quite accurate. The real Bowie is a very small unincorporated community with a population of 447. It was named after the Fort Bowie ghost town.
John Rambo was born on July 6, 1947 to R. Rambo and Marie Drago. He is of American Indian (Navajo), Italian and German descent. His family was poor, often unable to buy food, and his mother died when he was young. His father was an abusive alcoholic who once tried to kill John with a knife. Rambo ran away that night, but not before shooting his father with a bow and arrow, nearly killing him. Rambo decided that the best way to get away from his problems was to leave for the Vietnam War, for which he had been drafted.
Rambo was seen at a prison quarry presumably located in Arizona at the beginning of the film. When Murdock reads Rambo's credentials, he mentions that he is from Bowie, Arizona.
When Hamid asks Rambo where he is from, Rambo replies that he is from Bowie, Arizona. Hamid asks how long of a walk Arizona is from Afghanistan and Rambo replies that it is about three years away by foot. Directly after this, Hamid then asks to see his knife, which is, ironcially enough, a Bowie-style knife.
The film's climax at the end was filmed at the Yuma Indian Reservation in, oddly enough, Arizona.
Rambo again confirms that he is from Bowie, Arizona when Sarah Miller asks him where he is from. He claims that it is a "small place" and that he worked horses when he lived there a long time ago. When she asks of the wherabouts of his family, he responds by saying that he doesn't know if his father is even still alive. At the end of the film, Rambo does indeed return to his horse farm home in Arizona, showing Rambo's Arizona home on screen for the first time.
Any scene that takes place in the United States takes place in Bowie.