If you want feel like to be in Japan, Mitsuwa Market Place is the best.
(The picture left is one of their events to cut whole of tuna in front of the customer. It might seem like barbaric, but it’s common in our culture for selecting a real fresh Sashimi. And Just cut sashimi is the best.)
They have a shuttle bus from port authority; it’s around 30 min from the central Manhattan. The largest selection of Japanese food, include some food courts and daily products shop.
They have online store also (English OK)
Most of my Japanese friends go to Mitsuwa monthly and enjoy the atmosphere there.
It’s also became popular for non- JP, you can find many reviews here.