As shafts of fading autumn sun dance through a bank of clouds above the towering Washington Monument, my eyes are drawn eastward to the Statue of Freedom sitting high atop the Capitol Building.

David, my affable guide from Wisconsin, points to the 19ft bronze female figure that embodies the founding spirit of the United States.

“She faces east because the sun sets in the west,” he explains.

“So as long as she stands there the sun will never set on the face of freedom.”

My bicycle tour of Washington’s monuments and memorials is coming to an end and the observation merely reaffirms what became so apparent as I pedalled from one stop to the next through the leaf-strewn paths of the National Mall.

“There are no coincidences in DC,” David adds, flicking up his bike stand as he prepares to head back to base at Unlimited Biking.

“There’s a plan behind everything.”

Symbolism rules

Symbolism pervades the US’s capital city, and no visit is complete without a tour – by foot, bike or bus – of the familiar landmarks that chart the story of a nation through narrative architecture.

My highlight is standing on the granite steps of the Lincoln Memorial, looking out on the shimmering waters of the Mall’s vast reflective pool from the very spot where, in August 1963, Martin Luther King Jr delivered his era-defining ‘I Have a Dream’ speech.

Given its storied past, the challenge for Washington has always been widening its appeal beyond its rich heritage and attracting visitors keen to see something new.

The freshly reopened National Air and Space Museum is a fine example of how the city is attempting to balance its past with its present.

The collection houses some remarkable items, from the Wright brothers’ Flyer, which completed the world’s first manned flight, to the Columbia command module that brought the original lunar astronauts back to earth. Neil Armstrong’s Apollo space suit is also on display.

More than half of the 1,200 artefacts in the new section have never been exhibited before, including a full-sized X Wing fighter from the Star Wars franchise.

The museum is free, and for that you can thank an English chemist who never set foot in the United States.

James Smithson, who died in 1829, bequeathed $500,000 (£438,722) in his will to establish an institute in Washington that would promote the “increase and diffusion of knowledge”.

He had one stipulation – that entry would be forever free.

Air and Space Museum

As well as the Air and Space Museum, I visit the National Archives – where the Declaration of Independence, Constitution and Bill of Rights sit side-by-side – and the National Museum of Natural History, where giant model dinosaurs, whales, elephants and sharks provide a ‘wow’ factor for young and old.