if you are there for long duration then try some bike tour.
Your travelling plan is driving me crazy tho --------- Singapore> Mexico>now Japan

why in this order? I am guessing you are in business trip and not backpacking.
You still didn't disclosed about the " Surprise"

Its Golden week in Japan and its annual thingy.
-A bike ? People are crazy here, they drive on the wrong side of the road ! I'd probably get hit by a bus or worse by a Ferrari. Imagine that poor car ! Oh wait, where are you from again ?

-I know east > west > east again, that's exhausting ! I'm traveling with a group of 80 yr old people, they're all dead by now. Kiddin' of course.
-Well Tokyo is the surprise ! Isn't that enough ? Did you expect me to meet Godzilla, Satoshi... Craig Wright or Roger Ver ?

-Let's tell roach there's a silver week too, he'll move here. Naaa, the Japanese are good people, they don't deserve that.
@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.
I'm familiar with Ramen and yes they're the perfect food for me.
Veggie Miso is trickier I found out.
Thanks for the tips, I appreciate it ! I'll keep them in mind.