Thanks for the Airbnb suggestion. Only issue might be finding something large enough for 4 adults and 6 kids that isn't a luxury penthouse running $5,000 a night. This is still in the very early planning stages. I won't even know when I'll get my leave until sometime in early 2020 once I'm already deployed.
The reason we're looking at NYC is that there's a direct 4-hour flight from here and a lot of international flights go through NYC so there's more options for me to get back to the US from there. Plus, it would be a great experience for the kids to see things like the State of Liberty, 9/11 memorial, USS Intrepid, and a bunch of museums - to say nothing of the experience of just being in a huge city and riding on a subway.
I'm not familiar with how all the different mileage programs work. In the past I've had a Southwest Airlines credit card that basically gave enough free points for one or two tickets, but I don't want to be locked into a single airline. I'm not sure if my flight will be with Air France, Turkish Airlines, Ethiopian Airlines, or someone else. The bigger cost will probably be the tickets for my family. Right now it looks like JetBlue is the best bet as they offer a direct flight that's reasonable cheap. I see a lot of cards that offer 50,000 - 70,000 "points" but I'm unsure which of those points will convert into the airline miles or other travel rewards I'm looking to use.