Regent's Park
Laid out by John Nash from 1811 for a Prince Regent who never got round to building the palace it was designed to surround. It still feels designed: the Outer Circle, the rose gardens, the boating lake, none of it accidental. Four hundred acres, with London Zoo inside the north end and Primrose Hill just over the road.
Hapoo counts the walk you were doing anyway
Read off your phone's motion sensor after the fact, so there is no start button and nothing running in your pocket. Characters turn up at real park gates across London, this one included.