Washington is plonked down in the District of Columbia, a little enclave chopped from the state of Maryland. It is bounded on one side by the Potomac River (on the other side of the river you'll find Arlington and Alexandria, Virginia) and on the other sides by the state of Maryland. The city covers 170 sq km (65 sq mi).
Washington is ringed by a freeway bypass called the Beltway, which divides the urban insiders from the suburbanites. The Capitol isn't just the symbolic centre of Washington: from here the city is divided into four compass-point quadrants along axes following N Capitol St, E Capitol St, S Capitol St and the Mall. Identical addresses appear in all four quadrants, so you need to know the directional component of the address you want.
Streets are arranged on a grid of north-south numbered streets and east-west lettered streets. This grid is overlaid by broad diagonal avenues. The geometric pattern is further interrupted by traffic circles that add to the city's appeal but can make DC a challenging place for outsiders to navigate by car.
Most tourist sights are located around the Capitol, along the Mall and in the Northwest quadrant. Downtown includes the monuments dotting the Mall but is otherwise strictly business. Dupont Circle is an upscale business and residential address with a groovy fringe; Adams-Morgan is bohemian, funky and international; Shaw has historically elite residential areas and ghettos, and Georgetown has pristine historic houses, a university and lively bars. With Northwest quadrant real estate spiralling out of control, Brookland and the Northeast quadrant are showing promising development.