Japanese food is great, but sometimes you want a taste of home. I wanted to make certain dishes, such as lotus root soup, which my local supermarket didn't have the ingredients for. So I went to check out Asian grocery stores in Shin-Okubo and Ikebukuro.
The main thing to note is that most of these grocery stores do not sell fresh produce, unfortunately. This means I have been unable to obtain many ingredients like winter melon or shark fin melon (not actually made of shark fin). I would most probably have to make a trip to Yokohama's Chinatown to find them.
The first place I stopped at was 華僑服務社, a Chinese grocery store. They have multiple floors in the building, one of which is just for frozen food. It is also the only place I know of in Tokyo, other than the airports, that sells Shiroi Koibito, as you can see in the picture below.
This is the biggest store that I went to. They have a good selection of Chinese sauces, seasonings, frozen food (e.g. mantou or fatty pork), and dried goods like red dates and vermicelli. It's also a good place to get Chinese snacks and alcohol. For products that can be found in normal Japanese supermarkets, like dried shiitake mushrooms, they're probably cheaper here.
I also went to Asia Superstore, a Thai grocery store. This is one of the rare ones which sell fresh produce. I saw produce like lemongrass, galangal and whole coconuts. I was also very happy to find Thai jasmine rice, as I have not been able to find non-Japanese rice at any Japanese supermarkets. I like Japanese rice, but because the flavor and texture are different, it just doesn't go with certain cuisines, like Southeast Asian cooking.
Besides produce, they have a good selection of Thai and Southeast Asian spices and seasonings. I bought oyster sauce, green and yellow curry paste, and a spice mix for a stew dish.
In Ikebukuro, I went to Youyi Asian Market. It's rather small, so it probably doesn't carry anything that 華僑服務社 doesn't have. But it is convenient if you're in the area.
They have a small frozen section, and a selection of seasonings, dried goods, snacks and alcohol. The store owners also speak Chinese, so they can probably help you with looking for something obscure.
I ended up buying red dates to make soup with, dried shiitake mushrooms because they were cheap, and some soybean milk to try. (It ended up being too sweet.)
Another place I visited, but which isn't a grocery, store was a Malaysian restaurant fittingly known as Malay Asian Cuisine in Shibuya. Besides selling authentic Malaysian cuisine, they carry a small selection of Malaysian and Southeast Asian products, like chili sauce, frozen roti canai/roti prata, and curry mixes.
I hear Ueno is also a good place for Chinese grocery stores, but it's a bit out of the way for me, so I don't visit often.
Chinese grocery stores aside, my local supermarket, Summit, actually carries a decent of ingredients for Chinese cooking, like goji berries and star anise. So instead of travelling to a specific location, it might also be worth checking out the larger supermarkets in your area.