$6k mo is a bit high imo. $4500-$5500 should be adequate depending on family size. Downtown/Orchard road you're looking at $6k+. Airport, much less. East Coast in between. You can go north and west but what you save will be offset by higher cab fare. Then again, if you have children you may want to cut down on their bus ride by living closer to the school.
The idea that you must live near expats of your own nationality is a personal choice. It was not a prime consideration for me.
The training bond is what it is. Learn about it, and make your decision accordingly. I can honestly say it had no bearing on my decision.
Good luck!!