Tower of London
Natural History Museum
Wetland Centre at Hammersmith
Wembley stadium tour
Ice rink at Alexander Palace (or the temporary one at Kew Gardens or Somerset House which is there for Christmas)
Seeing the famous sites such as Big Ben, Houses of Parliament, Buckingham Palace, 10 Downing Street etc about 8 years ago
Hamleys, if you must go, is on Regent Street, more towards the top end (Oxford Circus end) but you could get off at Picadilly and walk up Regent Street and it would be on your right hand side.
As a child, I used to love my yearly trip to Hamleys and could spend hours and hours and hours in there. We also used to go and gaze at the christmas windows at Harrods and Selfridges.
I think I just used to love being in London as a child - we rarely went to a museum, but would always walk around and see the sights such as Big Ben, and as it was christmas time, the lights on Regent Street and Oxford Street were a must, followed by dinner in a long gone Italian restaurant just off the back of Picadilly Circus which is now a Boots! about 8 years ago