i know you said teaware, but if you want to look at a tea shop in tokyo, i'd check out thés du japon's new shop:
https://japaneseteasommelier.wordpress. ... ten-years/
also, i'm glad you're taking the time to ask people in advance. ime, showing up in japan and asking people where to find good tea and teaware
simply will not work. people will want to help you but won't be able to. most japanese people know little about tea and don't really care about it. to most there, it's just something to drink for free instead of water.
i wish i could tell you more places to go, but i haven't discovered them yet
unless you get specific recommendations, imo your best bet in general is to look for nice art/antique galleries. that's where i've seen the best stuff.
home goods sections of department stores were a waste of time for me.
if you go beyond tokyo... in kyoto, there are sweet galleries (like asahido -- some crazy antique tetsubin there) by the kiyomizudera. robert yellin's gallery is there as well.
tokoname is also a nice place to visit if you like tokoname yaki.
good luck, and let us know if you find cool places!