Adding my research here from after emailing and googling several of the Japanese dealers. Unfortunately I only did my research for Toyko.
Note that some of companies have a few different stores and not all locations stock melodica esepcially if youre looking for the PRO models. I believe most music stores should have the basic melodicas for schoolchildren but I cant confirm as I have never been to Japan myself.
1) Ikkebe Gakki
Emailed this store and their Kenbando store, just next to Shibuya train station is apparently the store specialized in Keyboard and should have most models here.
2) Ishashi Gakki
From what I understand they have a few stores in Japan. You can try emailing them as they responded to me in English, but I did spoke further as they didnt have the model I wanted.
3) Taniguchi Gakki
They have a specialized Accordion/harmonica/melodica floor here. Located just one station away from akihabara which is a very common tourist destination. Unfortunately I emailed them and received no response. They did have an english page which unfortunately also says they dont speak english so…. :/
4) Kurasawa Gakki
I only know they sell a few basic models and didnt do much research after that
5) Amazon Japan
Apparently I only realized after ordering directly from Amazon JP that my friend mentioned I could have sent it to a local 7-11 or other convenience store and have picked it up. However you might be charged the 8% local consumption tax and have no way of testing it beforehand.