This is the most genuine and unpretentious pub I have visited in London. The Palm Tree is on the east London canal outside of Victoria Park. You won't find it unless you know it's there. (And now you know!)
Brilliant Corners...Great sound system, vinyl only, dancing, left field, fourth world, jazz, afro, and some refreshing cocktails to help with all the sweating. Probably the only place i will actually dance in.
They also do amazing Japanese food earlier in the evening.
Walthamstow Wetlands are London's largest urban wetland nature reserve, home to many wildlife species. Only 15min from central London. The cafe is open daily for breakfast, lunch and afternoon tea.
Key community arts centre, near to Shoreditch High St station. The cinema is handy and the music programming is solid, but they also host a variety of other interesting nights, most notably Jawdance, London’s (arguably) best spoken word night
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.