British Museum
If you are only on a city break, then this should be one of your priority visits. Set near to Soho, the building itself has recently been renovated by Lord Foster so the 18th century golden stone contrast spectacularly with the modern glass dome built over the courtyard. Highlights inside include the ancient peat-bog man, the Elgin Marbles, and the Rosetta Stone from Egypt, but there's so much more and you could easily get lost for a week in there!
Admission: Free, but it is currently desperately short of donations.
Where: Great Russell St, WC1, 020 7636 1555, www.thebritishmuseum.ac.uk
Tube: Holborn, Tottenham Court Road, Russell Street
Open: Great Court Mon 9-6pm; Tue-Wed, Sun 9-9pm;Thur-Sat 9am-11pm. Galleries: Mon-Wed, Sat-Sun 10am-5.30pm; Thur-Fri 10am-8.30pm