Walk along Thames/get the bus/boat to Tower Bridge and go to Tower of London. Stop at Tate Modern on the way and larf at what passes for art.
Tube to South Kensington and museums (Science adn Natural History.)
Duck boat tour - goes from the road to the Thames, best to Google.
Walk over Westminster Bridge from London Eye and go to Covent Garden/Trafalgar Square/Leicester Square/Chinatown for lunch - no good if very wet.
Half price theatre ticket booth in Leicester Square if it's Wednesday.
IMAX cinema at Waterloo v close to the Eye.