I am not a proponent of the idea of just wandering around and eating whatever 'looks good' or is convenient. Sometimes it is inevitable, but if you want to explore a cuisine, then you need to take advantage fo the info out there.

However, if you only want to eat the familiar, then that is very limiting, as Japanese cuisine in the US or Europe is only the comic book version of what is actually prepared in Japan.

In Kyoto absolutely go to Sushi Matsumoto in Gion--- it's a 2 star michelin sushi restaurant and it is flawless. If you go for lunch it's about a 1/3 the cost of dinner with several of the same dishes ;) reservations essential

IL ghiotonne in kyoto is also absolutely amazing --- it's japanese Italian fusion (which I know sounds like a stretch) but it was better than several of the michelin restaurants we went to--- lunch was extremely reasonable $45 per person for 5 courses (including a wagyu beef course)

Mishimatei has some of the best shabu Shabu in kyoto... be sure to grab a slightly early reservation so that you don't get rushed out. Pricy but worth it

For good cheap eats try hisago in Gion

Thanks so much for taking the time to give me all of your advice and recommendations :) Truly appreciate it!

Nywoman- We thankfully were able to book a reservation Shirosaka in Tokyo. It looks like a wonderful meal; we're really looking forward to it. Thank you!

There's a restaurant called Zauo which is pretty cool. The area where you sit is shaped as a boat with water all around it. There are lots of fish in the water and you go fishing for a fish and they cook whatever you catch. It was a pretty cool experience.

One stop for a foodie to consider is the food floor at the Isetan department store in Shinjuku.