I think the asia pass (when its offered for sale) will not be worth it considering the surcharge to go to 60 or 90 days. It would be limited to 4 destinations and be upwards of $2k - but this includes your ticket from NYC to JFK. If you are traveling during summer (departing before Aug 15 IIRC) it will be especially not worth it.
IME NRT/KIX will be the expensive cities, and probably not worth it for a weekend.
Air Asia is like $200 a/i to BKK or KUL/ Jet* to SIN/Jakarta around the same --that is pretty cheap.
Getting from Kowloon-Shenzhen Airport is a lot easier now with direct busses - and you can get fares as low as $160 r/t ai to shanghai and ~$200 to beijing.