There's a good chance that you'll be tagged as tourists and taken the long way around on your way.
There is a flat rate from JFK of $52. Ask for that.
Or, actually, I would recommend you reserve a sedan limo (black car) in advance. They should run you about $60. I've used these guys before with success.
http://www.nycroyallimo.com/
Expected tip for either service (since I know you are probably not used to tip culture) should be around 15%. 25 - 30% if they give you excellent service (cab is clean, they handle your luggage for you in and out of the vehicle, they have a nice outgoing and pleasant personality that made your trip more enjoyable, etc...)
Tipping is NOT mandatory, and if you end up with a poor experience, do not feel guilty leaving less than 15% or even no tip. Do not tip up front. Keep the money for your planned tip folded in the palm of your hand and pass it to the driver (or allow one of your children to do so) upon completion of unloading at the end of your taxi ride.
This way you don't have to go fishing through your wallet for cash (and also showing everyone else how much cash you have in your wallet in the process). Hand them the money as part of a handshake / handoff and say "Thank you". That's all.
I'm not sure how long you are staying, but I'd again recommend the 7 day MTA pass (even if you are not staying 7 days). It's a great deal. And, since you are going to be in the heart of Manhattan, the subway will be of great convenience to you.
You'll find (compared to your public transit) that many of the stations are dirty and worn, and the cars as well. Google some
youtube videos of the New York Subway before you go to be sure you and your family will not feel uncomfortable in those environments.
That being said, the subway is remarkably safe. Just stay away from overly crowded trains, more for personal comfort than anything else. There are all sorts who ride the subway.
A few other pieces of advice (take them for what they are...you may find them silly...I'm not sure how many times you all have been over here)...
1) You'll want to carry ID everywhere, but don't carry your passport anywhere. It's actually New York State law that law enforcement may demand you must be able to provide photo identification, and you'll need it to purchase booze. Leave it in the room safe or better yet, in the hotel safe. I am not sure if the Australian Government issues passport cards (not just the booklet), if they do, get those. They'll work great! Otherwise, your Drivers License should work fine.
2) Tipping is reserved to cabs (15% of fare), (maybe) housekeeping ($1 per person per day), your doorman/bellhop ($3 per bag), room service ($3 per diner), bartenders (Whatever you feel like, 10 - 15% of tab), and wait staff at restaurants (15 - 20%). You don't need to tip everyone who does you a service.
3) Don't be afraid to go for a stroll. NYC is large, but it's a fairly safe city (at least the parts you'll likely be in). However, don't dress in a flashy manner, and I'd actually recommend not carrying a large purse. Rather, do a clinch or a nice leather backpack.
4) Buy a prepaid credit card for your daily use. Don't carry much cash. You can charge the card up with cash or credit cards or bank transfers online. But, you'll want to have pocket cash as well...just don't carry much unless you plan to go to the street markets or something.
5) You may want to consider buying a cheap pre-paid cellular phone when you get there. They are great to stay in touch, make local calls, etc...and you won't have to worry about international or roaming charges on yours. There are lots of carrier options, but MetroPCS or Boost Mobile are two I'd consider. Both networks have "unlimited voice/data" options for not much money ($45 or so) so you can utilize Google Maps when you are there, which could be a great benefit to you. While the city is largely a grid, and fairly easy to navigate, it can be overwhelming.
6) Don't hesitate to ask people things. The general impression that New Yorkers are anti-social and rude is simply incorrect. For the most part, they will be happy to help you all with directions, advice, etc.
Anyhow, brain dump done. Not sure what else to tell you at this point, outside of enjoy your trip! I'm sure you will, it's an amazing city!