Who do you trade with? IB has access to the futures on the exchanges in Japan and Singapore. Each of them has too big of a multiple for the underlying for me, though, hate to risk too much per tick when I'm just getting used to an instrument.
You could also trade the yen (with the USD pair or the EUR pair), it moves with a negative correlation to the Nikkei, with some upward bias lately. When the Nikkei takes its lunch break, the traders are still playing around with the ES and the YM in our AH, and the yen keeps moving with negative correlation to the direction of those.