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.
London is so vast I am forever coming across new hidden gems. Walking around the streets and getting lost is the best way to find London's best kept secrets.
I am definitely not precious about the materials I use to make my work, but every so often I find myself in need of something more specialised. L.Cornelissen & Son is a beautiful and well stocked art supply shop with extremely knowledgable staff.