In addition to what's also been mentioned, I'd also highly recommend:
Trattoria Raffaele for some great pizza from a local family run business.
http://trattoriaraffaele.com
The Lemon Tree for what i think is the best indian food in Sydenham
Sugahill for the best paninis and hot chocolate in London
Agas deli/Little Cafe for by farther best coffee and cakes on the planet (seriously, I've never tasted cakes as good as hers).
Kirkdale Books (say no more)
Mustis pound shop for an aladins cave of stuff
The Bath Store in Bell Green for second hand architectural salvage
On the Hoof in the station for great coffee
Home Park for it's outdoor gym
Mayow park for it's cricket and playgrounds
Sydenham Library for it's cafe and kids events