I've been to Japan a few times now and I've been cancelling and moving my next flight forward a few months for the last 12 months.
The food in Japan is on another level from anywhere else I've been, it stands to reason really as of the top 5 cities with the most Michelin stars, Japan holds 3 spots with Tokyo at #1. However, for street food I'd say that Osaka is better than Tokyo. Off the top of my head, the food to check out would be...
Street Food
Taiyaki - a batter in the shape of a fish with all filings under the sun, sweet red bean paste, custard etc.
Takoyaki - octopus in batter balls covered with mayo, sauce and katsuobushi (shaved dried fish)
Kani - grilled spider crab legs
Yakitori - fried chicken skewers
Doriyaki - pancakes with fillings in the middle
Dango - rice flour balls
Matcha ice cream
Kakigori - shaved ice, in the oppressive summer (or even the warm autumn) this is so good!
Restaurant Food
Okonomiyaki - savoury pancake with loads of options of fillings and toppings
Tendon - Tempura donburi, it sounds bland but it's so so good!
Kaiseki - Traditional multi-piece meal with so many seasonal dishes of whatever is in season and fresh, I usually don't know what 50% of the stuff is but it's all amazing
Unadon - Unagi donbori - grilled eel on rice, don't let the image of jellied eels put you off, this is probably my favourite dish though a bit pricy at around £30-£40 for a serving
Sushi
Ramen- so many types but tonkotsu (thick pork broth) is my favourite
Tsukemen - like ramen but the noodles and broth are separate, you dip the noodles in the broth
Kariraisu - curry rice, Japanese curry is different to Indian curry but also really good, you can usually add toppings like soft boiled eggs and cheese too
Kushikatsu - breaded and fried stuff on sticks that you dip in sauces
Wagyu steak - doesn't really need much explanation, be prepared for it to ruin all future steak for you!
Gyutan - beef tongue, this is the speciality in Sendai and is actually really good despite the name
In terms of places I've been to, they all have their good points, if you have any questions let me know:
Tokyo - So many things to see and do, though Akihabara was a bit overhyped especially if you're not into anime or manga which I'm not. Shinjuku is definitely my favourite part of the city with so many things to do.
Osaka - amazing city and you're more likely to end up chatting and drinking with the locals
Kyoto - you can spend days walking around here looking at all the shrines, temples and old streets
Hiroshima - super friendly and laid back city with good okonomiyaki, it's also close to Miyajima island and the famous shrine (one of the 3 top views of Japan)
Kusatsu Onsen - an amazing place to just chill out in all the onsen and rotenburo (outdoor baths),
I stayed at a ryokan owned by a guy who had spent a few years in London so it was good to chat to him and get some good local tips, it's also not too expensive
Nikko - Super old and historical town, not many foreign tourists but loads of local tourists
Sendai - The biggest city in Tohoku and a good base to head out places like Matsushima below
Matsushima - small coastal town near Sendai with an amazing view (one of the other top 3 views in Japan)
Morioka - Small town with a few interesting things to see, I mainly went as it's my friend's hometown