A couple of years ago I visited New York and to be honest it was overwhelming. Even with the aid of a good guide there was so much to do and see that the only places I actually got to visit were the touristy bits like the World Trade Centre and the various department stores. I wish I'd had a New Yorker show me around town or, at least, a list of places they'd recommend visiting.

I live in London and have done all my life. Here's just of a few of the places I'd recommend a tourist visits. Some are popular with tourists, some are not.

Tate Modern - A wonderful building full of wonderful art. Puts your faith back into modern art and Britain. The ill-fated Millenium Bridge stands outside. Maybe it'll be open some time soon?
Nearest Tube Station: Southwark (Jubilee Line)
Admission fee: Free (all donations gratefully received)

Ronnie Scott's - A jazz cafe in Soho. Every time I go I'm amazed and delighted by the talented musicians who play here.
Nearest Tube Station: Leicester Square (Northern and Piccadilly Lines)
Tickets: £5-£20 depending on act

The 5th Floor, Harvey Nicholl's - Straight out of Absolutely Fabulous. A pricey but outstanding resturant.
Nearest Tube Station: Knightsbridge (Piccadilly Line)
Avrage 3-course meal: £30-£50 excluding drinks

Cyberdog - A small clothes label, with stores in Covent Garden and Camden. I love their clothes, everything is bright and fun.
Nearest Tube Station: Covent Garden (Piccadilly Line)
Clothes: Roughly £20 for a t-shirt to £150+ for some of their wilder creations.

Fabric - One of London's 'Super Clubs'. Some wonderful dance music is played here.
Nearest Tube Station: Farringdon (Bakerloo, Hammersmith & City and Metropolitan Lines)
Ticket prices: £12-£25 depending on acts

Solid Sunday, The Mean Fiddler - Quite a way off the beaten track in Neesden but if you enjoy house music then this is one to visit. Very popular with Australians and Kiwis, the place has an absolutely amazing atmosphere.
Nearest Tube Station: Willesden Junction (Bakerloo Line)
Prices: £3 before 5pm, £5 after.

Victoria and Albert Museum - Probably my favourite museum in London, situated in Kensington near the Natural History and Science Museums. Full of stuff the British stole from other countries when we were busy doing that empire thing.
Nearest Tube Station: South Kensington (Circle & District and Piccadilly Lines)
Admission Fee: Free

London is a big place and these are only my personal favourites. Ask around and you might find somewhere a bit more interesting than Buckingham Palace to visit.