The Barbican is worth visiting for it's brutalist architecture alone. The concert programming is really diverse; it's home to the BBC Syphony Orchestra, but you'll also find bands like the Dirty Projectors and the National amongst the classical and contemporary composer line up. Plenty of art, dance and theatre too, however, the Conservatory is the real gem that's not to be missed.
This beautiful 19thC industrial building is situated in Markfield Park just around the corner from my studio. Once a sewage treatment works serving the whole of Tottenham and now a museum. The fully restored Victorian pump engine is only open to the public on the second Sunday of every month but the outside of the building and surrounding park is a worth a visit regardless.