The quiet route from South Norwood Lakes to South Norwood Country Park.
Goat House Bridge is pretty nasty. You may want to dismount and walk this bit.
Croydon council decriminalised cycling in parks and on railway paths some years ago but never got around to taking some of the old signage down - cycling past Love Lane Green etc. is fine and lots of people do.
From the Country Park there are lovely routes north (Waterlink Way via Ancaster Road - to Beckenham, Lower Sydenham, Catford, Lewisham, Deptford, Greenwich), south (NCN 21 towards Shirley / Ashburton) and south-west (quietway route through Addiscombe to East Croydon).