Not intended to be exhaustive - this is just my round up of what I have come across after 13 months of living in Tokyo.
Last Updated: December 2014.
Shinjuku Craft Shops - I created a map and list of shops for a tour I did. download .doc list and descriptions and download .doc map
Nippori Fabric Town - Blogged about here. Worth going to just for Tomato which has four different buildings.
Yanaka - as well as having a comic museum and an amazingly beautiful sculptor's house which is always worth visiting, and lots of cats and cat merchandise, it has a beautiful bamboo craft shop called Midoria (3 Chome-13-3 Nishinippori, Arakawa-ku). This is high end stuff so you can easily pay 15,000 for a woven vase but they also have smaller, cheaper items. Beautiful work. Few minutes walk from Nippori station, in the opposite direction to Fabric Town.
Sakura Horikiri - washi paper, fabric and paper 'painting' and kits galore in Asakusabashi. Eveything is in Japanese but the staff are very friendly and the kits are so well illustrated it is clear what you need to do just from the pictures.
Kiwa Products - beads and findings for jewellery, resin craft, bag making and probably much more. There is a small one in Shinjuku but the store in Asakusabashi is enormous - about 5 floors of lovely temptation and tonnes of instruction sheets at 50 yen a time if you lack a definite plan. There are a lot of bead shops in this area - look out for 'wholesale only' signs as they won't welcome you.
Traditional Dolls - if you are in Asakusabashi to visit either of the two above places you really have to go and at least have a quick look at the ground floor of this place. Kyugetsu is one of several of these places in the area and the dolls are just amazing, and I'm not into dolls at all. If you walk from here to Sakura Horiki you'll go past another doll making shop with all the bits and bobs needed to get started.
Salvation Army Bazaar - it might sound odd but this huge charity shop is a warehouse with different sections for clothes, books, furniture, crockery (just get everything here rather than at IKEA) and also crafts. I've blogged about it here. Only open on Saturday mornings but definitely worth a visit. Buttons are so expensive in Japan so this is a great place to get them.
100 Yen shops - beloved beauties. The biggest I've found is Daiso in Harajuku (blogged about here and in picture below).
Online craft shopping in Japan - I compiled a list of places I found out about at the Yokohama Quilt Show here. I also have a list of places selling finished handmade items in my Handmade in Japan Fes post here. Okadaya and Yuzawaya (in the Shinjuku download) also have online shops.
Pottery - Shirokane Ceramic Art School. I have done their 'try out' class in english and it was awesome. I had never made anything on a pottery wheel before and it was a great experience. Wear trousers you don;t mind getting clay on (it washes off easily). Don't expect a modern studio. It is off the main road and down a traditional little street.
Loom Weaving and/or Indigo Dyeing - both at one place, Wanariya in Asakusa. While this is a child friendly activity, don't be put off by the pictures of children on the website. I still felt like a grown up while weaving and am ridiculously proud of my coasters. You can also take your own fabric to indigo dye and they charge you by weight. About 15 mins walk from the station. Very friendly people.
Washi Paper Mini Tasters - the shop at Sakura Horikiri (above) usually has a little taster session going for some form of paper craft.
Adhoc Craft Meet-ups - meetup.com is very active in Tokyo. I can recommend Kokoro Crafts Group!
Tokyo International Quilt Festival - blogged about here. Held in January every year at the Tokyo Dome which is a huge baseball stadium. This show gets seriously busy - as in no-room-to-turn-around busy. You save a couple of hundred yen and avoid the queues if you buy a ticket in advance. Not as many shopping stalls as I would expect but amazing quilts - if you can get close enough to see them!
Yokohama International Quilt Week - blogged about here.
Handmade in Design Fes - blogged about here. A staggeringly huge event by british standards.
Design Festa Tokyo - I hear this is very good.
Other big events - keep an eye out on Time Out Tokyo for what is going on.
Stitch n Bitch Meetup - a very active group with people passing through and some 10+ year regulars. All nationalities welcome. You just promise to buy one drink minimum wherever it is, although the food at Pariya is delicious if they are there and you should try the ice cream too. There is a daytime group as well as this evening one. Both meet twice a month. I found out so much about craft shops, dealing with the recycling and more from chatting to regulars at these meetings.
Searching google in Japanese - an artform in itself. If you can't find something by googling in English, it is quite easy to do so in Japanese. The key to success is using Chrome as a broswer which auto-translates for you. Then go to translate.google.com and type in what you want to search for (i.e. glass blowing lesson ガラス吹きレッスン) and copy and paste the japanese into google.com. Each result will then have "translate this page" as a link next to it. Click on that to see what the suggested websites are saying.
Time Out Tokyo - keep an eye out for flea markets, big events, museum exhibitions and so on.
Japan Folk Craft Museum - amazing exhibitions in the most beautiful traditional building with a rotating collection of handmade items.
Bunka Gakuen Costume Museum - blogged about here. An often overlooked simple but quite large museum near Shinjuku station. They have exhibitions on all sorts of fashions.
Tokyo Crafts Gallery - This comes under the wing of the National Museum of Tokyo but is in a separate building. It is a great space and has some excellent exhibitions.