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
This independent cinema near Angel in North London is over 100 years old and has had several lives including hosting early Sex Pistol gigs. It now serves as my favourite place to watch films (along with the Rio in Dalson).