Fans of Blow Up will appreciate this.
From Central London, find your way onto the eastbound Jubilee Line and go to North Greenwich. Go upstairs to the bus station (good place for a shit) and catch a 422 or 486 from stop B - very frequent and they start from there. They both land you at a stop in Upper Charlton called 'Cemetery Lane,' arrowed on the map.
From there, follow the Green Chain Walk signs (towards the Thames Barrier) down through Maryon Wilson Park, past the animal enclosures, across a rollercoaster of a minor road and into Maryon Park, the scene of the crime and a very good place for a shit. The first sight of the tennis court is your cue to relax and explore and muse on how the lens alters our perceptions. Think beautiful thoughts about Vanessa Redgrave and be guided by the excellent signboards.
When the party's over, keep heading North, across the railway bridge, and you will soon hit the Woolwich Road - very big, you can't miss it! Do not cross the road, just find the nearest bus stop and catch a 161 or 472 back to North Greenwich tube.
3 hours round trip plus exploration/chillout time onsite. Zones 1&2 Travelcard covers it.
Extension: instead of just catching a bus back from Woolwich Road, do cross it and continue following Green Chain Walk signs North towards the river and the Thames Barrier. From there you can walk along the river back to North Greenwich tube, passing the Anchor & Hope pub along the way. If you're unlucky, their resident standards singer will be serenading you over much of this stretch. Her voice travels far - be sure to travel further.
Extra 1 hour plus exploration time for this option.
Keen cartographers will realise that the aforementioned 'rollercoaster' road is used by bus 386 from Woolwich, a very useful way to go, that Cemetery Lane bus stop can be reached in the opposite direction by routes 53, 54 and 422, also from Woolwich and that Woolwich Arsenal is, in fact, an excellent alternative railhead for this round trip, as is Charlton, amongst others, especially for people based in East or Southeast London. Congratulations! You have outgrown this site and are well on your way to becoming a Route Ranger in your own right.