I know this comment comes from a great contributor of this forum and it is written with good intentions, but I find it a bit patronizing... maybe the OP has already seen all of that! We do not know. And if he or she wants just to do pen shopping, it is his/her choice. I have been in Japan twice over the past two years and I was able to do both, extensive pen shopping and time to appreciate the cultural beauties of the country. The two activities are not really mutually exclusive in my humble opinion.
There is bias in my suggestion as vintage pens are more my interest. There are vintage pens to be found in antique shops and flea markets. Rarely have we invested the time and energy. Much ahd to do with schedule. Once, we found a large quantity of older Platinum ephemera. Usually, a few 1950s Pilots. One of my friends in Tokyo has great connections with flea market sellers and always has a few pens to share with me.
We visit Japan every year and always find new and interesting things to do. Two times we combined pen hunting with tourism. Before leaving America, we created our itinerary based on visiting places that had out of the way pen shops. If you hunt hard you can find two great shops in Kyoto, and others in Wakayama, Nagano, Kanazawa, Sendai, Aomori, and Gifu. My best source was a small shop in Kochi.
Much depends on your focus. Only one time did I find something sooooo special in Tokyo that I had to buy it. Rarely have new pens sparked my interest.
Patronizing. Hmmm! If the latest greatest obscure color Pilot 747 or super-duper nibbed Sailor 9000 makes your day, go for it. If you can save $35-$40, great. For ink, I have never seen anything so special or unique in using funny colors or squid ink. Pens are writing instruments - utilitarian objects. There are some that have collector value and appreciate over time. Many makie, for example, fall into that category.
Ten years from now 90% of those participating in this group will no longer have any or have interest in fountain pens. That is a fact. Wherever we go, we try to not take our hobbies or baggage with us. Work is difficult to leave behind. It may seem we can go anywhere and visit any pen shop we like in Japan. Not the case. We wish to thoroughly use the limited time available to enjoy ourselves..