Have a fun trip! You might want to check out this list that Fudefan created https://www.fudefan.com/buy-from-jp/ or
https://estilofilos.blogspot.com/p/tokyo-pen-shops.html
(which is by the author of the Chronicas Estilographicas blog, which you will enjoy and find a great resource). It's a bit older, but includes the discount shops in Tokyo's Ueno-Ameyokocho market (cash only).
Tokyo Inklings is a podcast you might enjoy for more info on Japanese pens and stationery world. Check out old episodes to find things of most interest.
I also suggest the video series that the Wet Pen created on YouTube about searching for custom inks in Japan. Of course many of those shops sell fountain pens. He also has reviews of papers, as does Blake's Broadcast. More fun informative videos on shops and the like with https://www.youtube.com/c/InkyRocks.
If you don't speak Japanese, you are more likely to be able to have more support with trying different nibs in a shop at large stores or airport shops.
Depending on where you will travel (and your Japanese ability), I found that you can get more help at smaller locations. The Itoya HQ in Ginza is wall to wall people these days, but I was able to spend a lot of time at Itoya's Yokohama branch which was in the Takashimaya Department Store at Yokohama Station. It is quite small, but was more relaxed. I don't recall if anyone spoke English though. If you do duty free, I think you have to get that handled at the main Duty Free office in the basement.
I am happy that you have Lichtope on your list. It is a bit hard to find unless you use Google Maps, but the woman who works there is a wonderful nibmeister who speaks English very well. It is a nice walk to Daikanyama, which is also home to the Tsutaya T-shop, which is an amazing bookstore/office goods shop. Fun neighborhood with many places to eat too.
You might call to make an appointment and make sure Lichtope is open. The same goes with Eurobox too.
For vintage pens, it is a bit harder to find at brick and mortar shops. Kingdom Note in Shinjuku has several, but I imagine they get raided online quickly.
Since you are quite interested in Japanese pens, you might enjoy browsing 趣味の文具箱. My library gets the magazine via the Libby app. With the online version you can try using a translation application. It has reviews, news, info on shops, nibs, papers, inks and the like. It is a bit of work, but is an interesting Mook (book/magazine) and shows the passion of Japanese fountain pen fans. Speaking of Japanese fans, there is a fun YouTube series by Penguindo in Japanese, but you can create subtitles in English using the settings option. She shares trends like the upcoming price increase, but more fun things too.
Paper is a big topic. I like writing lots of notes, so I'm a big fan of getting sets at MUJI. Doodlebud has reviews (like this one), but beware that MUJI has different paper options and labels are not always helpful. Different locations also have different stocks. I picked up a set of something like 5 notebooks for less than $10. I use them all the time, but I use an EF nib and sensible ink.
Kokuyo's CAMPUS notes are also good and affordable. You can have fun visiting their CAMPUS shop in Shinjuku if you have time. They also have airport branches. Even their basic paper is good for me. Your mileage may vary. Nemosyne and Tsubame and others are great. Most lines have grids and different size rules and blank papers so do try them out. You can also find nice Bank paper and Iroful and the like. Even some of the notebooks at Daiso/100 yen shops are not too bad. Some are bad though. One can spend a fortune on notebooks if price is no limit. I love the APICA CD notebooks for more serious writing.
OK, that should give you enough things to explore before you go. Have fun. Enjoy exploring nibs. I also like the FA and SU and EF nibs.
(I imagine you like EF nibs, so if you want to try something American I suggest the Esterbrook with cool independent nibmeister special grinds, like the Journaler. You can also get their adapter to use their vintage nibs. I just ordered their MiniStub and am looking forward to how it works. Aloha!