Go on the London Eye, visit a Museum, go round Camden Lock market, take a boat trip along the Regents Canal, take a boat trip to Greenwich, or go on the Docklands light railway to Island Queens and then walk the old tunnel to Greenwich, visit Highgate Cemetry, go round the Tower of London, go shopping in Harrods, go to Pollocks Toy museum, go to Covent Garden, or failing all that, buy a copy of Time Out and see what is on.
hmm, yes, it is always difficult to find anything happening in London. But I love the way you can stroll in and out of galleries like the V&A and the National Gallery, British Museum and Museum of London because they're all free.