Sydenham Hill Woods is a lovely area of woodland for walking in. It's quiet and peaceful, even on the weekend, and popular with dog-walkers and young families. It's big enough that you're not endlessly coming up against fences with roads on the other side of them, yet small enough that you can't get lost there. It's also the most pleasant way to get from Forest Hill to East Dulwich and when you do get to the Dulwich side, there is a marvellous area of pretty allotments to wander around, from which you may take in 'the best view of London in London'.
From the Forest Hill end, it's about a ten minute walk from the train station. The 185 and 176 buses also stop nearby.
Is this your business?