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Join Date: Feb 2010
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You could not be more central, and that hotel has its fans (though I personally prefer the Hilton Metropole).
Well here's my semi random top six suggestions:
1) British Museum - which is free-ish
2) London Eye - go in the evening when the queues are less
3) Choral Evensong at St Paul's / Westminster Abbey / Southwark Cathedral /etc - make sure there's a proper choir in though!
4) West End play or musical / National Theatre
5) Early morning walk around the medieval areas of St Bartholomew's Hospital / Smithfield.
6) Mid morning walk from Trafalgar Square, through The Mall, Buckingham Palace.
Basically I would treat it as a test run for a proper visit to London. It's an amazing place.