Hi Mlee,
I would possibly suggest that you grab a copy of a Japan guide book, like Lonely Planet Japan. This has suggestions on different types of restaurants in each area of each city.
For recommendations on the web wikitravel usually has a few mentioned for each suburb, for example:-
http://wikitravel.org/en/Shinagawawww.bento.com also has a huge range of options depending on what you like.
I also like exploring and going to a restaurant that looks interesting and/or busy. We've found many favourites by just wandering near the hotel/station and then eating wherever looks the best! Tokyo is obviously a huge place, so if you can perhaps narrow down where you are staying it might make suggestions easier.
We like eating different foods each night, so a few on your list could be:-
Udon/Soba, Okonomiyaki (in Osaka), Yakitori, Sushi (Tsukiji fish markets Tokyo), Takoyaki (snack in Kyoto/Osaka), Sukiyaki/Shabu Shabu, Yakiniku, etc.
Pious, not sure where you are in Australia, but there are a number of Japanese restaurants on the Gold Coast and Brisbane that serve all of the items you listed, Takoyaki, Okonomiyaki, Green tea Ice cream, pickles and a reasonable variety of sashimi including for example uni (sea urchin). Maybe we need a new thread, favourite Japanese restaurants in Australia :)
Enjoy your trip Mlee!