Yes of course, Greg, this is a "pretty silly thread". That was its intention -- you can imagine my surprise when I logged back in to discover that some people thought it was a genuine and very serious enquiry... But at least it shook Jeff Brauer's list out of the tree, which some appear to have enjoyed, so...
Bradley Anderson hits on the head what led to me thinking about the topic, though. If you find the phrase "green complex" wanky (and maybe it's just that I can't grow a beard for shit, so I have nothing above the belt to stroke while I say "green complex") then simply saying "green" leads people to think you're referring to the putting surface in isolation and "green site" seems to refer only to the piece of ground upon which the green and green complex are built.
JLahrman got us the closest to something -- the "neighbourhood" suggestion.
"Greencock" wasn't bad either.