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.
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
Quinto sells second-hand books. I spend a lot of time here and have found some inspiring books over the years, both at Quinto and the other shops on this road. Koenig Books on the corner is good for art books, too.