Availability: end of October – February 2017 (no holidays)
Search on google flights [google.com] for date availability, then plug dates in at Priceline [priceline.com].
My sample travel dates: Jan 13-20, 2017 via Delta Airlines
Alternatively, All Nippon Airways, a more superior airline in terms of service & quality, will be starting new NONSTOP service from ORD and JFK to Haneda beginning October 30, 2016. However, price for that is about approx $ 992 roundtrip.
Unfortunatlely, Google flights is not showing the $ 521 (it is showing $ 667) dates so when on Expedia [expedia.com], choose departures of Tues, Wed, Thur, Sun (no mid Dec – mid Jan)
Fare Availability: Tuesdays & Wednesdays, October – December 13, 2016
Book on American Airlines [aa.com].
Please note that while this fare is valid at time of posting, fares can fluctuate in a matter of minutes/hours/days.
My sample travel dates: Oct 25 – Nov 1 (LGA-ORD)