I'm travelling to london for a couple of days ...

The big ban! Kidding, it's individual. If you like art though, the Saatchi Gallery is brilliant.

There is a lot to see and do in London, enough to fill more than a couple of days. I would consider it a pity if someone had been to London and not seen some of world famous musems -  the British Museum (even briefly), the Natural History musem. Also I would recommend the Tower of London (plus the houses of parliament), Westminster Abbey, Tower Bridge. London is also world famous for its theater and night life,  I would suggest making an effort to see one show at least. You can check out

If your trip is over a weekend, as well as hitting the museums and main sightseeing spots, head for Borough Market near London Bridge station.  It's the city's oldest food market, and has a fantastic selection of food stalls at the weekend.  Then from there you can walk along the Southbank of the river Thames to get some of the best views of the city across the river - it's particularly beautiful at night.  You'll go past the Globe Theatre, the Tate Modern gallery (converted from an old power station), the Millennium Bridge (a foot bridge which you can go across to get a great view of St. Paul's Cathedral), and then get to the Southbank arts complex which has the Royal National Theatre, the Queen Elizabeth Hall and then the Royal Festival Hall (London's premier classical music venue).  This gives you a great sample of all of the oldest and newest architecture that the city has to offer, along with some of the more diverse folk to rub shoulders with along the way. 

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There is SO MUCH to see! What a brilliant city this is.  The way to see as much as possible in as little time as possible is to take a taxi tour of London.  If you go with an established taxi tour company, like London Black Taxis, their drivers are also qualified tour guides who know the city better than anyone.