Washington was founded as a political capital in 1791. Its location was chosen by the man whose name it takes, George Washington, at a point between the established cities of the north-east and the Southern states. It occupies its own zone (the District of Columbia), independent of the 50 states, hemmed by Virginia to the south and Maryland to the north – at the confluence of the Potomac and Anacostia rivers.
The centre spreads out around the National Mall (nps.gov/mall), a two-mile grassy strip that ebbs east to west as it plays host to the country's most significant monuments and museums. Beyond, the city is organised into a simple grid. Streets that run south to north are numbered (eg 14th Street), while major east-to-west avenues bear letters (such as F Street).
Take a hike
The National Mall demands a morning of your time. Start at the Washington Monument (nps.gov/wamo), the 555ft obelisk that honours the first US president. It was damaged in the earthquake that hit the city last year and its public gallery is currently shut. But even from the ground, it's an impressive sight.
Head west to the National World War II Memorial (nps.gov/nwwm), where each of the 4,048 gold stars represents 100 American war dead.
Continue west on Independence Avenue SW as far as the Martin Luther King Jr Memorial (nps.gov/mlkm). Then turn right on to West Basin Drive SW and right on to Ohio Drive SW for the Mall's two most eloquent monuments: the Franklin Delano Roosevelt Memorial (nps.gov/fdrm), where arty sculptures acknowledge America's wartime leader, and the Thomas Jefferson Memorial: a statue of the third president stands proud in a Neoclassical temple (nps.gov/thje).
Track back to the west end of the Mall – to see the ghostly soldiers of the Korean War Veterans Memorial (nps.gov/kwvm); the iconic steps of the Lincoln Memorial (nps.gov/linc); and the Vietnam Veterans Memorial (nps.gov/vive).
Then dart east on the top edge of the Mall, turning north into the green space of The Ellipse – where the pale celebrity of the White House does not lack visual impact as it sits at 1600 Pennsylvania Avenue NW.
F Street is a neat encapsulation of Washington's retail scene. Chas Schwartz & Sons (16), at 1400 NW, is Washington's oldest jewellers, dating to 1888 (chasschwartz.com). And Fahrney's Pens, at 1317 NW, has been dispensing writing equipment and ink to politicos since 1929 (fahrneyspens.com). If you prefer your ink invisible, the International Spy Museum, at 800 NW (spymuseum.org; $18/£11), has a shop that's a den of gadgets.
Lunch on the run
Enjoy a slice of Americana at Ollie's Trolley, a classic US diner at 425 12th Street NW (olliestrolleydc.com).
Take a ride
Visit Bike and Roll at 1100 Pennsylvania Ave NW. Rental starts at $12 (£7.50) for two hours, $30 (£19) for a day (bikethesites.com). Pedal west along the National Mall and over the Potomac on the Arlington Memorial Bridge. At the end, you drop into Virginia – and find the gates of Arlington National Cemetery.
A walk in the park
There is a moving calm to the main US military graveyard (Memorial Drive; arlingtoncemetery.mil; daily 8am-5pm). John F Kennedy's resting place, on Sheridan Drive, is positioned so that it gazes at the Lincoln Memorial and Washington Monument.
Dining with the locals
Ben's Chili Bowl at 1213 U Street NW (benschilibowl.com), hit the headlines in January 2009 when Barack Obama ate here. Its chili half-smoke (a hot dog) is $3.25 (£2). Off U Street at 2007 14th Street NW, Marvin serves a chic take on soul food (marvindc.com), with chicken and waffles for $17 (£10). Back in town at 480 7th Street NW, Jaleo (jaleo.com) sells tapas such as cod loin with parsley sauce for $12 (£7.50).
Go to church
The National Cathedral lurks a fair trek from the centre at 3101 Wisconsin Avenue NW (national cathedral.org); take the Metrorail Red Line to Tenleytown station. Sunday services are at 7.45am, 8.45am, 10am and 11.15am.
More convenient is St Patrick's Church, at 619 10th Street NW (saintpatrickdc.org), an 18th-century refugee founded in 1794 with a cool interior of marble and stained glass (Sunday services 8am, 10am, noon).
The Smithsonian is the world's finest cultural collective – 18 museums, many based on or around the National Mall. All are free, share the same basic contact details (si.edu) and are open 10am-5.30pm daily, unless stated.
Focus on the institutions that do something unique: the National Museum of American History (1400 Constitution Avenue NW; americanhistory.si.edu), which displays exhibits from first ladies' ballgowns to early Apple computers and Ford motorcars; the National Air and Space Museum (6th Street SW and Independence Avenue; airandspace.si.edu), where you can see the Wright Flyer alongside Apollo 11 artefacts; and the joint American Art Museum and National Portrait Gallery (F Street and 8th Street NW; americanart.si.edu; npg.si.edu; 11.30am-7pm daily), where art by Hopper and O'Keeffe hangs with official portraits of each president.
Out to brunch
At the excellent National Museum of the American Indian (4th Street and Independence Avenue SW; americanindian.si.edu) the Mitsam Native Foods Café serves bowls of thick buffalo chilli for $7 (£4.50).
Icing on the cake
Ford's Theatre at 511 10th Street NW (fords.org), where Abraham Lincoln was assassinated in 1865, still stages plays. Tickets for the latest production, A Christmas Carol (Till December 30), cost from $51 (£32).
(Chris Leadbeater/The Independent )