Is there a word for "love of open spaces"?
As distinct from "love for public spaces" which I understand agoraphilia to mean. Since I think the Greek agora means an "assembly" or "market place"; not "open spaces".
If by "open spaces" you mean areas away from buildings, a possibility is outdoorsy.
dictionary.com
unusually fond of outdoor life:
an outdoorsy type who always swam before breakfast.
Oxford Living Dictionaries:
Of, associated with, or fond of the outdoors.
‘Bill is such an outdoorsy kind of guy’