In the south east quadrant:
Titsey Hill/Titsey Road between the Botley Hill pub and Limpsfield - lots of fun in the southbound direction;
Chelsfield Lane just south of Junction 4 - this is very quiet;
Crockenhill Lane just south of Junction 3 - useful for getting to/from the Darent Valley lanes from the city side.
Titsey Hill is quite busy though. Not so bad going down but horrible to come back up (and it's bloody steep).
I used to cycle out from Coney Hall (Hayes) via Gates Green Lane – continue due south (Jackass Lane, ha) to Downe (home of the jackass) and keep going onto Cudham Lane South, then the Nower and down Brasted Hill which slips over the M25 and into Brasted. And you are free. I'd loop around and visit some friends in Sevenoaks (skip this portion, they don't know you) and then come back via Darent Valley and the Crockenhill Lane route from Eynsford (this has the benefit of being a route back over the North Downs with very modest gradients).
Further west from Titsey (oh, be quiet at the back), there's a couple of routes down from the North Downs (on road, Chalkpit Lane, some traffic but not so bad, or Tandridge Hill Lane and Flowers Lane). There's a nice amble along route 21 through Woldingham School to get there. You can follow route 21 all the way from Greenwich but be wary that there are regions of this bicycle route that are, erm, unsuitable for bicycles (steep gravelly paths etc, may be OK if your mountain bike skills are topped up or you're willing to occasionally push – oh, and there are gradients).
For less glamour, there is actually a shared pavement down the A22 that gets you under the M25. Abandon the A22 ASAP thereafter though, it's hell.
West of the A22, there are a couple of lanes (Whitehill Lane and Warwick Wold Lane) that get you over or under the M25. Fine for descent, but I'd wouldn't try and clamber back up them, they pick up some – oft impatient – traffic trying to avoid the M23 and the M23/M25 junction. If you don't mind a few bumps, the descent along route 21 isn't too bad unless you have very skinny tyres, but bear in mind if you plan to return that way that there are loose surfaces and a steep gradient). For approaches, you can again keep to the 21 which crosses a bridge over the A22 (gird yourself for a steep climb on the other side). Or from the other direction, take the pleasant ride from Coulsdon up over Farthing Downs and the Happy Valley – Ditches Lane, Church Lane through Chaldon, and Hilltop Lane, turning left onto the Pilgrim's Way when you see the sign. Or drop down Warwick Wold Lane. Wheeeeeeeeeeeeee.
