The oldest public art gallery in London also is my local gallery in my neighbourhood. Opposite to the Dulwich Park where I walked with my puppy regularly. They have great collections of Dutch paintings as well. My husband found the original Dutch painting of the print at his home he was growing up with.
The Party Superstore was/is my absolute favourite London shop until it was bizarrely attacked and gutted during the summer London riots. They have been since adopted as a concession by the local Debenhams but you can still savour the full delights of the products and nonsense on line.
Founded in 1828 the museum houses around 67,000 specimens many of which are now extinct or endangered. My favorite is the skull of a Bottlenose Whale from 1860.
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.