A few thoughts:
http://www.beefsteakandburgundyclub.org.au/
Changi Sailing Club (I've heard it's pretty relaxed for a 'yacht club')
http://www.csc.org.sg/
http://www.rotary.org.sg/
Plenty of golf/country clubs, but that's not my thing, so can't comment further.
As you suggested, getting their foot in the door at ANZA might open up all the opportunities from there that they need.
My own parents did a relo to be near the grandchildren and help out (and later be helped themselves in return). It is vital (in my opinion) that they get socially engaged from early on. Or the danger is that the family becomes their sole focus, and this can become a bit overbearing. It seems it can be harder for older men to make this adjustment. You know what they say about old men being happy sitting in their garden sheds all day long, well it's true I think, but it's not healthy
Just my 2c!