The Old Post Office Tower
If you want nice
views of the city from on high without waiting in long lines to go up the Washington Monument, the
Old Post Office Tower is your ticket. The tower is the 3rd tallest structure in the city. Riding to the top is free, and the only wait is for the elevator (there is rarely a line). You do have to go through magnetometer and put your bag through an x-ray machine, but it's not too much of a hassle.
Getting there is pretty easy. The building is located at Pennsylvania Avenue and 12th Street NW in Downtown Washington. From Union Station, you can take the Red Line to Metro Center and exit to 12th Street to walk a few blocks south. Or at Metro Center you can transfer to the Blue/Orange Line and go one stop to Federal Triangle, which is directly across the street from the Old Post Office. You could also walk or bike. It's 1.3 miles from Union Station. And there's a bike rental place right next to the station (on First Street NE @ Massachusetts Ave).