It was 50 years last year since Martin Luther King Jr made his rousing "I Have A Dream" speech, and the latest memorial on Washington's National Mall pays tribute to the Civil Rights leader. It's a powerful piece, with a 9.1-metre likeness of King carved out of white granite – that's the Stone of Hope emerging from the two blocks behind that represent the Mountain Of Despair. The memorial is surrounded by quotes from King, and the man himself crosses his arms to look out over the Tidal Basin.

2 The other memorials

The Lincoln Memorial, of course, is where King made that speech. An engraving commemorates this on the spot where he stood. But it's perhaps the more underrated of the memorials that have the most impact. Franklin Delano Roosevelt's works like a storyboard – you walk through the events of his four terms in office – while the Korean War Veterans Memorial features dead-eyed soldiers edging through a battlefield.

3 Spy Games

Nowhere is riddled with espionage quite as much as Washington DC – and the International Spy Museum revels in it. It's a gloriously entertaining romp through all the gadgetry used by spies throughout history, featuring all manner of elaborate cover stories and disguises. The museum also puts its name to tours of the city's key spying sites – including the infamous Watergate Building and the former Soviet Embassy. Featuring video "briefings" from former intelligence officers, the tours are packed with intriguing Cold War tales and anecdotes. See  spymuseum.org

4 Georgetown

Many of those key spy encounters took place in well-heeled Georgetown, which likes to think of itself as separate from the rest of the city. It's a handsome area of red-brick Victorian houses, canal-side walks and quality restaurants. But amongst the evocatively refined atmosphere is some seriously good shopping. Classy boutiques line M Street NW and Wisconsin Avenue – with a great mix between fashion, homewares and gifts. There's nowhere better for a sunny afternoon's mooch.

5 JFK sites

Also in Georgetown is Martin's Tavern, where John F. Kennedy popped the question to his then girlfriend Jacqueline Bouvier. It's been a popular spot for proposals ever since – ask for Booth three if you want to get engaged in the same place. JFK's grave can be found just over the Potomac River in the Arlington National Cemetery. It's marked with an eternal flame. Jackie, and two of their children who died during infancy, lie beside him. Martins-tavern.com, arlingtoncemetery.mil

6 The National Archives

This pompous neo-classical monster hosts many oddities. It's where important and not-so-important documents related to American history are collected, but the big three really put a frog in the throat. There's the Magna Carta, the Declaration of Independence and the US Constitution – three documents that act as a global mission statement for the principle of democracy more than any others. There's a real sense of significance, even though you're ushered through with unseemly haste. Archives.gov

7 Cherry blossom trees

Springtime sees Washington – and the Tidal Basin in particular – turn pink. It's all thanks to Japan, which made a gift of 3000 cherry trees in 1912. Since then they have become something of a Washingtonian symbol. The two-week Cherry Blossom Festival in late March and early April uses the burst of colour as a good excuse for a party. Expect kite-flying displays, mass moonlight walks and parades. nationalcherryblossomfestival.org

8 The Washington Monument

Standing in the middle of the National Mall, no building in Washington DC is allowed to be higher than the 169-metres-tall Washington Monument. This means the giant stone obelisk stands out from miles around – particularly at night when a red aircraft-warning light flashes and gives it a somewhat sinister look. Alas, it's currently under repair after earthquake damage in 2011, so visitors are not going to be allowed up until everything's fixed in 2014.

9 The Smithsonian Museums

When British scientist James Smithson died in 1829, he left a will bequeathing his estate "to the United States of America, to found at Washington, under the name of the Smithsonian Institution, an Establishment for the increase and diffusion of knowledge among men". It's one of the world's more extraordinary gifts, and the Institution now covers 19 museums – all of which have free entry. Of those clustered around the National Mall, the Hirshhorn Museum and Sculpture Garden is great for modern art, the National Museum of the American Indian covers native cultures and the National Museum of Natural History is dinosaur-tastic. si.edu

10 The National Air and Space Museum

Deservedly the most visited of the Smithsonian Museums, however, is this giant magnet for aviation geeks. There are some phenomenal exhibits in there – including the Apollo 11 command module and the Spirit of St Louis, in which Charles Lindbergh made the first successful non-stop transatlantic crossing. If you don't come out wanting to be an astronaut, your inner child has officially died. airandspace.si.edu

11 The Newseum

Not all of Washington's Museums are free, and if you've got to stump up for one, make it the Newseum. It's a six-floor exploration of the news – both the stories and the people who get them. Highlights include finding out how the media has reported on and shaped presidential campaigns, a moving section on the September 11 terrorist attacks and an extraordinary gallery of every photo to have won the Pulitzer Prize. newseum.org

12 Mount Vernon

Sixteen miles south of the city, Mount Vernon was the home of the first president of the United States, George Washington. It has a gorgeous setting looking out over the Potomac River, with sprawling gardens on the old tobacco plantation. The tour of the Washington's home is only mildly interesting – seeing the president's deathbed is the highlight – but the Reynolds Museum and Education Center offers a greater insight into Washington's life and the difficulties he had holding the fledgling nation together. The issue of slavery – Washington owned slaves all his life – isn't glossed over, and the slave quarters near the house can also be visited. mountvernon.org

13 Ford's Theatre

Another great president met his end at Ford's Theatre, where John Wilkes Booth shot Abraham Lincoln. The exhibitions downstairs go into the assassination plot and the hunt for the conspirators afterwards, but they're far more interesting when they're exploring Lincoln's life and presidency. A shrewd, often Machiavellian character emerges – but one who managed to (eventually) bring about the abolition of slavery and keep the country together through the Civil War. fordstheatre.org

14 The White House

1600 Pennsylvania Avenue is arguably the world's most famous address, and the White House looks as impressive in real life as it does in the movies. Sadly, you can't just wander into President Obama's house to have a poke around, but it's possible to stare through the gates. The White House Visitor Center nearby goes into the history of the building, showing the changes each president has made to it, and discussing the quirks of trying to have a normal family life surrounded by the media and big security teams. whitehouse.gov

15 Ethiopian food

One of the most unexpected things about Washington is the number of Ethiopians who live there – and that translates to lots of excellent Ethiopian restaurants. 9th Street NW has a large concentration of them, including Etete, which offers a range of hugely tasty, spicy stews to be eaten with injera – spongy flatbread – instead of cutlery. Dukem on U Street offers similar dishes, as well as live entertainment. dukemrestaurant.com 

16 U Street

It's not just Ethiopian food you'll find on U Street – Chinese, Thai, Jamaican and pretty much every other cuisine you can think of is in the mix. Traditionally an African-American area, in the era of Duke Ellington and Cab Calloway U Street was known as Washington's Black Broadway. It's now hugely multicultural – ironic gay sports bars mix with pubs that use profits to build schools in Africa – but a series of signs explaining the history make for a fascinating self-guided walking tour.

17 The Capitol Building

The home of the US government's legislative branch is open to visitors – you can sit in on Congressional debates when the House of Representatives and Senate are sitting. But the tours of the building are more interesting than political waffle. Constantino Brumidi's frieze around the central Rotunda, showing George Washington becoming a god, is both wonderful and curiously against everything the American revolution stood for. The Hall of Statues – featuring two choices from each state, and some controversial ones amongst them – also has a fabulous air of grandeur. visitthecapitol.gov

18 The Library of Congress

Just opposite the Capitol, the Library of Congress should be an obligatory pilgrimage site for any bookworm. It's the largest library in the world, with over 150 million items in the collection. Of these, some of the stars are on display to visitors. These include the first world map to ever feature the American continent, and one of only three perfect copies of the Gutenberg Bible. It also hosts frequently rotating exhibitions that present the treasures thematically. loc.gov

19 Happy hour drinking

Washington is a lot livelier than its reputation may suggest – but it's not a late night party city. The time to go out drinking here is after work, particularly around Capitol Hill where Congressmen, political staffers and various hangers-on head for a few happy hour drinks that often turn into a few more later. Pull up a barstool at 5pm, get chatting to whoever ends up next to you and you'll more than likely hear some good gossip.

20 The Steven F. Udvar-Hazy Center

Washington Dulles may be outdated and a nuisance to get to – it's 42 kilometres west of the city – but it has the world's greatest pre-flight time killer next door. The Steven F. Udvar Hazy Center is an often ignored branch of the Smithsonian, and houses a staggering collection that includes the Space Shuttle Discovery, a Concorde, a stealth reconnaissance plane and the Enola Gay – the aircraft that dropped the atomic bomb on Hiroshima. airandspace.si.edu/visit/udvar-hazy-center

The writer was a guest of Destination DC