Agree with Freeagent
“Chislehurst, Bromley Common, Petts wood, Farnborough, Keston are the nicer parts of the Borough, New Addington/Biggin Hill not so much “
Locks bottom is also a good spot as is Crofton.
I grew up round Farnborough village way .. very nice and easy access to Orpington station with quick links into London.
From a riding perspective you have heaps of great road routes out into Kent and Surrey but MTB is slightly limited depending on your stance about riding on footpaths (still better than most London boroughs IMO)