City of London - The Square Mile, London
THe Barbican Centre is an impressive venue in the city which runs a year-round programme of art, music, film and theatre and it is also home of London Symphony Orchestra.
Beneath the Guildhall there are the remains of the original Roman Amphitheatre - as well as the computer generated model of its appearance!
Look at the old light well - this used to be open to the sky but they roofed it in and made it a place you can hire out. Local artists provide the basis for the works of art.
A great hotel. Go in and take the lift to the 6th floor. Look at the rotunda (some call it the Little Guggenheim, others the Polo mint). Believe it or not, you can't actually walk down it!
The City is the financial district in London. There are major companies headquarters here as well as the Bank of England including a museum about British financial history.