It depends what kind of thing you like. The Victoria and Albert museum is quite good for a mooch. Some exhibitions are free. The Natural History Museum accross the road still has the Wildlife photographer of the year exhibition on. There`s a new Watercolours exhibition at the Tate Britain. Camden market is good to wander around. That`s on saturdays and Spitlefields market in Greenwich is good on a Sunday. There`s always the London Eye, Harrods, Liberty etc. If the weather stays as pleasant as it is today the parks would be nice to wander in too.