Cafe Zaiya (more like a Japanese deli): I've been a loyal customer of Cafe Zaiya's since I moved to New York from Japan 4 years ago. Their midtown location (E. 41st St btw Madison and Fifth Avenues) is the best and biggest.
http://www.zaiyany.com/

Panya Bakery
http://www.yelp.com/biz/panya-bakery-new-york

Takahachi Bakery
http://www.yelp.com/biz/takahachi-bakery-manhattan

Cha-An Teahouse: I go there often.
http://174.132.150.226/~sobayany/ct/site/index.html

ChikaLicious: You can enjoy their dessert course! Chika-san's desserts are amazing.
http://www.chikalicious.com/

Minamoto Kitchoan
http://www.kitchoan.com/E/index_b_natsu2004_e.html
Now you will be introduced to Takoyaki たこやき。
There are two kinds of takoyaki.

This one is sometimes called tamagoyaki, and you can find it easily in the Kobe area.
http://www.youtube.com/watch?v=fpB1DQ9eRAE&feature=player_embedded

This video (Kono bideo) has translation in eigo (English).
http://www.youtube.com/watch?v=PHDmVhShE80

This takoyaki stand is from Shimane しまね my home prefecture.
http://www.youtube.com/watch?v=fRiHfS8Z65Y

Every festival in Japan has at least one takoyaki stand.

Again, you can try takoyaki at OTAFUKU おた福
Eline's lesson
http://www.youtube.com/watch?v=GSyWxtSSKIE&feature=related

This is another video where you can see how kore, sore and are are used. The food that the two female students are making is called "okonomiyaki (おこのみやき: お好み焼き)". It's Japanese pizza (maybe pancakes), and I highly recommend it. You can try some at OTAFUKU (おたふく), a take-out restaurant, near NYU ( East Village, Manhattan). Otafuku's okonomiyaki (otafuku no okonomiyaki おたふく の おこのみやき) wa maa maa desu (まあまあ です)。 Many of us (Japanese people) consider "okonomiyaki" as one of our favorite foods, and we often have an okonomiyaki party. おこのみやき は とても おいしい です。(Okonomiyaki wa totemo oishii desu; okonomiyaki is very tasty). Osushi おすし and tenpura てんぷら are not the only Japanese foods!!
http://www.youtube.com/watch?v=B4gKy3UwVOE