Coming here as a child and even now the collection is utterly astounding I can spend hours in the fossel and mineral room. Plus the architecture of the building is completely unique and breath taking.
The walk along the South Bank from Westminster to Tower Bridge will take you past a plethora or interesting sights and cultural hotspots. There's always something interesting going on too.
The Wellcome Collection is a free museum and library, mostly dealing with medecine and social history. The exhibitions are unusual and engaging, and the permanent collection includes bizarre items such as medieval masks and human remains.