There is more than one location in the City associated with The Duke of Wellington and waterloo.

The Waterloo campaign of 1815 was without exception the most famous of the Nineteenth century.
It was to culminate in the final overthrow of Napoleon Bonaparte by Wellington and the end of twenty five years of warfare.
The London home of the Duke of Wellington. Apsley House.
 

The Wellington Museum 149 Piccadilly, London W1
Wellington Arch: London’s famous landmark at Hyde Park Corner.

There is a exhibition inside the Wellington Arch telling the story behind the monument, with excellent views of the city skyline from the viewing platforms above.
Not to mention a close up look at the great landmark sculpture (Peace descending on the Chariot of War) atop the arch.
Open daily from 10am until 5pm. Admission Details Adult £2.50 Child £1.30
Concessions £1.90
Location: Wellington Arch Hyde Park Corner W1 Telephone:+44 (0)20 7930 2726
Richard Westmacott's statue of a nude Achilles is the dominant feature of the Wellington Monument in Hyde Park Corner.
Achilles was cast from cannons captured in the Duke of Wellington's military campaigns.

Background
On 15 July 1815, Napoleon was exiled to the remote tiny volcanic island of St. Helena, south of the Equator.

Napoleon was buried on St Helena, but his body was later reburied in Paris on the banks of the Seine.

The Battle in Literature: The Battle of Waterloo figures prominently in literature.

It is an important feature of the epic poem Childe Harold's Pilgrimage (1818) by the British poet Lord Byron, and the poetic drama The Dynasts (1908), by the British author Thomas Hardy.

The battle is also an event in the plots of the novels The Charterhouse of Parma (1839), by the French writer Stendhal; Vanity Fair (1848), by the British author William M. Thackeray.