South Norwood Country Park
A cycle or walk through this pleasant country park in Croydon. National Cycle Network Route 21 runs around the park on nice traffic free paths. The park includes a pretty lake with lots of wildlife to look out for.
To extend your exercise head north to Cator Park in New Beckenham. Here you can pick up the Waterlink Way which takes you to the River Thames on a series of traffic free paths.