Lizby,
If you get club membership (or even not) as part of your package look at the Polo Club as one of your options. I only went a couple of times as a guest, but it seemed very quiet and spacious...with of course - horses.
An area you might like to look at re a yard is Clementi - a little area where (I think) all the streets have Sunset in the name.
It certainly would be very convenient to Jurong, I am not so sure re SAS - anyone?
It really does look like a regular Western suburb in the middle of Singapore. Lots of expats and dogs!