Green Park

The plainest of the Royal Parks, and deliberately so: forty-seven acres of grass and plane trees, with no lake, no fountains and no flower beds anywhere in it. The land was a burial ground for lepers from St James's Hospital in the Middle Ages, which is the reason everybody gives for the missing flowers and for which there is no evidence at all. Charles II enclosed it in 1668 and walked it every day; the route he took is still called Constitution Hill. Daffodils in spring, and the quietest of the central parks to cross on a weekday morning.

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.