Day 1: Royal Botanic Gardens, Kew, TW9 3AB http://www.kew.org/
Bring lunch with you

+ a good dinner in China Town

Day 2:
AM
Boat to Greenwich and tube back
Walk around Westminster to see the Big Ben etc
Walk to St. James Park + Beckingham Palace
Walk to Hyde Park, have lunch there then walk around (can see the Royal Alber Hall, looks quite nice from outside)

PM: Walk south: many things on the Exhibition Road

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See the museums, bookshops and galleries in London if it rains.

Or go shopping.