When your movie is based on a non-fiction novel, you want it to maintain as much realism as possible.
Alan J. Pakula filmed as much as possible in Washington D.C., showing us exterior shots of the Watergate Hotel and the U.S. Capitol. Pakula even enlisted actual Watergate guard Frank Wills to play himself discovering the break-in. (Side-note: someone should make a movie on Wills' life.)
Any non-D.C. locations (like Miami) were actually shot in Los Angeles. And the Washington Post's offices had to be re-created because the Post wouldn't allow the filmmakers inside. Even with these locations, though, the filmmakers strove for authenticity. Trash from the actual Post newsroom was shipped to the soundstage in Burbank to put in prop trashcans. (Source)
One man's trash is another man's movie prop. Now that's attention to detail.