The best place to buy souvenirs in Tokyo is Asakusa
I would guess the number of foreign tourists and residents that visit Asakusa is near 100%. One can find souvenirs and gifts covering the full range of Japanese culture from paper fans, to lacquerware, to katana, to real kimonos. If you are a foreign resident of Tokyo, if you have any Japanese friends, one of the first places they will take you is Asakusa. Likewise, if you are a longtime foreign resident of Tokyo and you have friends or family visit you from abroad, no doubt you will in turn take them to Asakusa. This is how it worked for me.