Locations to visit
These links are to websites relevant to each of the listed Locations. Whilst not the only ones or even the best, they are intended to be representative.
City of London Commons
The City of London has several locations which are within the London Boroughs of Croydon or Bromley but only one outside, namely:
The National Trust was founded in 1895 and is now a registered charity. It protects open spaces and historic properties and makes them accessible to the public.. However, for present purposes, it is the countryside which is of interest. See their website for more details of who they are and what they do. For those more interested in the properties and in particular, refreshments available at those locations, there is an interesting independent blog which is not restricted to Surrey. Here are National Trust areas of open land in the county.
River Wey and Godalming Navigations and Dapdune Wharf - Really, a canal-side walk rather than open land although some sections are just that.