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New York City (JFK) – Haneda, Japan (HND) $ 521 on China Eastern Airlines via Expedia [expedia.com], roundtrip, including taxes/fees. Makes a layover in Shanghai, China (some layovers is long enough to make this 2 trips in 1)

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)