Since it is hard to know your tastes, I would suggest you visit any major department store basement to sample what interests you. Ask what it is, then search on your own. The okonomiyaki in Hiroshima is great, cooked in a different style than in other regions.
Just as a note, it is improper there to walk and eat at the same time.
I really like Japanese pickles. I hate US pickles, but the stuff you find in Japan is usually great. Go to the lower levels of department stores (wherever their supermarket section is) and usually you can find vendors selling a wide variety of foods, often with samples. The only place I know in particular is in Himeji (a city you should visit if you can); the Sanyo department store (just north of the station) has a really nice vendor with a wide variety of Japanese and Korean pickles (including a variety of kimchee).
You should eat okonomiyaki in both Osaka and Hiroshima. It's different in both places. You should also try senbei (rice crackers); most stores have them (even convenience stores). I also suggest finding a festival and sampling the various foods available there; the Web site for the Japan National Tourist Organization (www.jnto.go.jp/eng) has a good listing of festivals.
if u are going kyoto in summer, the matcha ice (i can't remember what it is called) is a must. It is a mountain of ice soaked in green tea and sweet milk, hiding a scoop of ice cream and red beans. Of course, the matcha tea is a must, you won't find anything close to it outside Japan!
Also try to find a restaurant selling Matsu beef. It is supposed to be even better than Wagyu and as sublime as foie gras. My one regret was not having tried it in Japan.
Lastly, if you are able to communicate to the sushi chef at a bar, try ordering seared toro sushi. Once again, one of those melt in your mouth experiences you'll never get outside Japan, unless you are willing to dish out big bucks for a top Jap chef to do it for you!
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