Horniman is great - including the aquarium and gardens. Dulwich park has a great cafe and playground and also you can hire bikes, including ones with buckets the little one can be pulled along in - www.londonrecumbents.com Brixton Rec is close and has good softplay - ball pit and big foam blocks for the little one, and kind of a climbing labrynth of tunnels, towers, ballpits, slides and shoots etc for the bigger ones. Borough Market - unless the 9 year old is a budding Gordon Ramsey/Nigella, I'd give it a miss. It's a cool place for adults but as far as kids can tell it's a bunch of grown-ups staring at cheese. Locale by Goose Green is very child friendly, even in the evening, Pizza Express is usually chocca with kids at lunch times and so is the Greyhound in the Village. Finally The Herne on Forrest Hill Road is very child friendly and has a great big playground out the back which is normally stuffed with kids. Ours loves it, as evidenced by her recently having to be dragged away from it whilst shouting at the top of her voice 'I WANT TO GO TO THE PUB!' If something not local was allowed to go on the list I'd add the basement of the Science Museum - very good with lots of things the kids can build, and sand/water they can make a mess with etc plus the rest of the museum is great too, and it's all free