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.
A walled secret garden, the Physic Garden is like a time capsule, founded in 1673 to allow apprentices of the Worshipful Society of Apothecaries of London to study the healing properties of plants, it is now a living museum. Tours are offered by volunteers with immense knowledge of botany and the cultural history of the garden or visitors can wander the grounds alone and spot odd and fascinating plants such as the mystical Mandrake.
I can't pass without dropping in, Orcs Nest is a small independent boardgame, D&D etc store that's been around forever(1987)... and has the best logo. Good selection of games for younger kids too.