Answer by taking a quote from the following article:

Annie Get Your Gun is a musical with lyrics and music by Irving Berlin and a book by Dorothy Fields and her brother Herbert Fields. The story is a fictionalized version of the life of Annie Oakley (1860-1926), a sharpshooter who starred in Buffalo Bill's Wild West, and her romance with sharpshooter Frank E. Butler (1847-1926). The 1946 Broadway production was a hit, and the musical had long runs in both New York (1,147 performances) and London, spawning revivals, a 1950 film version and television versions. Songs that became hits include "There's No Business Like Show Business", "Doin' What Comes Natur'lly", "You Can't Get a Man with a Gun",

In 1999, a new production had its pre-Broadway engagement at the Kennedy Center, Washington, D.C., from December 29, 1998 to January 24, 1999. Previews began on Broadway on February 2, 1999 at the Marquis Theatre, with an official opening on March 4, 1999, and closed on September 1, 2001 after 35 previews and 1,045 performances.  This revival starred Bernadette Peters as Annie and Tom Wopat as Frank, and Ron Holgate as Buffalo Bill, with direction by Graciela Daniele, choreographey by Jeff Calhoun, and music arrangements by John McDaniel. Peters won the 1999 Tony Award for Best Leading Actress in a Musical and the production won the Tony for Best Revival of a Musical.  This production had a revised book by Peter Stone and new orchestrations, and was structured as a "show-within-a-show", set as a Big Top travelling circus. "Frank Butler" is alone on stage and Buffalo Bill introduces the main characters, singing "There's No Business Like Show Business", which is reprised when "Annie" agrees to join the traveling Wild West show. The production dropped several songs (including "Colonel Buffalo Bill", "I'm A Bad, Bad Man", and "I'm an Indian Too"), but included "An Old-Fashioned Wedding". There were several major dance numbers added, including a ballroom scene. A sub-plot which had been dropped from the 1966 revival, the romance between Winnie and Tommy, her part-Native-American boyfriend, was also included. In the 1946 production, Winnie was Dolly's daughter, but the 1966 &1999 productions she is Dolly's younger sister. In this version, the final shooting match between Annie and Frank ends in a tie.

Where did the broadway take place?
Previews began on Broadway on February 2, 1999 at the Marquis Theatre,