Clime is variously defined as a place with a certain climate (MMD), or a place in reference to its climate (ODO), or a place where the weather is different in a particular way (CDO), or indeed to a climate itself (MW).
Clime in contemporary English is limited to poetic, or at least literary uses; meteorologists and travel agents do not customarily speak of climes. But with that in mind, know that clime is not limited to literal references to geographic locations and their weather, but can refer to the metaphorical meanings of climate— a prevailing condition or set of attitudes in human affairs (AHD).
Golden generally refers to some apotheosis or ideal: not only a golden age but the golden touch, a golden voice, and so on. (Descriptions that refer to the actual metal are simply gold, like gold coins or gold jewelry).
Thus, a golden clime refers to perfect social conditions, or an ideal intellectual atmosphere, or generally the best possible society for the boy to have lived in.