@Kenzawak
I strongly recommend getting a bowl of Kitsune Soba/Ramen/Udon, whichever noodles you prefer. I think they're vegetarian (might have to double check the broth depending on the place), but they use deep-fried tofu as a topping. And unlike regular tofu it actually has flavour. The frying process turns it into some kind of sponge that sucks up all the broth. Love the stuff.
Agedashi-dofu and -mochi are fantastic too. Fried tofu/mochi with usually some sort of bell-pepper sauce.
Curries are great too with all sorts of toppings, can recommend CoCo Ichiban blindly.
Vegetable Tempura just works for anyone. Can never go wrong with anything deep-fried.
Nasu Dengaku - Miso-glazed eggplant.
As far as Miso soup goes, I'm sure you'll find some that is vegetarian. I know that a lot of restaurants use shredded shrimp to give it some seafood flavoured kick, but a lot just use Konbu only.
There should also be some varieties of vegetarian ramen/soba and rice balls (fried or non-fried).
Anyway, just some of the non-meat/non-fish dishes that stood out to me while there.