Abakhan Fabrics has the best remnant bins in
town. The loot varies, but there's often good quality wool (solid
colours and plaids) in 3-5 m pieces. Cotton velvet and brocades are
also common as is cheap veil weight netting (my bridal veil came from
here, all the materials cost less than a meter of netting at home). It
also pays to take a look at the fabric sold by meter, in June they had
a very nice reasonably lightweight linen for sale. If you like
"modern" embroidery, Abakhan has a reasonable selection of cotton
aidas and suitable linens. As far as I know, the shops at Tartu mnt 58
and Pärnu mnt 69 are (unfortunately) closed on Sundays. You can
pay at Abakhan with a Visa, other credit cards may or may not
To get to the Pärnu mnt shop, grab tram 3 or 4 towards Tondi at Viru or Vabaduse Väljak ("Freedom square") and get off on the stop "Vineeri" (second stop from Vabaduse Väljak, third from Viru). The stop Vineeri is right in front of the shop.
To get to the Tartu mnt shop, try tram 4 towards Ülemiste and get off on Tartu mnt on the stop Autobussijaam (I think this stop is closest), near the central bus station. This is fourth stop from Viru, seventh stop from "Vineeri" in front of the other Abakhan.
Kangadzungel at Tartu mnt 49 is a funny fabric shop without display windows stuffed into an old movie theatre abt 10 minutes walk from Viru square. It seems that their fabrics are more suitable for mundane/modern clothes (lots of sweater knits, cotton prints and printed polarfleece), but the selection of trim is quite usable. It's also easy to browse as a samples of trim are fastened on cardboard, sorted by type and price. This shop is open all weekdays (Mon-Fri 9-19, Sat-Sun 10-17); there's another shop at Mustamäe where I've never been, and that one is closed Sundays.
All the shops of the fabric shop chain Kangas ja Nööp carry a selection of cotton embroidery floss, one skein usually costs 8 EEK (55 eurocents). These shops also sell an Estonian brand 100% wool yarn suitable for knitting for 24 EEK/100 g. If I remember correctly, the biggest Kangas ja Nööp on Kadaka tee (close to Eesti tekstiil) also sell Novita's (a Finnish brand) Estonian-made yarns; the prices are supposed to be somewhat lower than in Finland.
There's a specialized knitting yarn shop Filati on Müürivahe 20 in the Old Town (when coming in on Viru street from Viru hotel, turn left). The shop sells a wide selection of Italian Filati yarns, which are not cheap, but different from what you get for example in Finland. The shop is open 7 days a week.
I haven't been there yet myself, but according to a Finnish knitting enthusiast's pages, Veta at Pikk 6 (in Old Town) sells (mostly Russian) wool, cotton and blend yarns. Apparently they also sell some linen fabrics.
The department store Kaubamaja near Viru hotel at least used to carry DMC floss as well in its "home" department ("Kodumaailm") on the second floor of the B wing. Last December one skein cost 8 EEK (abt 50 cents), the metallic threads cost 15 EEK (1 euro), about (or less than) half the price one pays in Helsinki.
The ceramics sold by Mõisakeraamika at Sadamarket at the port (straight at the door closest to the terminal buildings) are good for SCA use and fairly inexpensive. They also seem to take some rough handling, haven't managed to break my goblet yet.
If you like modern art glass and ceramics, the place to go is Katariina Käik, ("Katariina's Passage), a narrow passage that starts at Vene 12. The shops Savikoda, Domini Canes and Klaasikoda sell glass and ceramics and even make things to order (but apparently it takes a while to get them, the talk on the net says "up to 6 months").
The restaurant Olde Hansa sells copies of all the glassware and ceramics they use. Some of these used to be available directly at the factory, but it merged with another firm and apparently the selection isn't quite the same any more (and the location has changed, too, somebody mentioned something about the port).
If you want to buy a pair of mittens or a knitted sweater, the place to go is Müürivahe just inside the Old Town. The easiest way to find it is to approach on Viru street; if coming from the hotel Viru (the city), turn right just after passing the gate in the old Town wall. Huddling against the wall there's a row of market stalls, all selling knitted woollens.
The price of a sweater at least used to be abt 500 EEK (abt 32 EUR), mittens and socks start from abt 100 EEK (6.50 EUR). The price range is pretty much settled, but the colours and the patterns vary, so take your time to walk past all the stalls and then turn around and ask for prices of what you like on the way back (you can try haggling a bit, but not too hard, it's not a custom here).
Fancier stuff can be found in the several craft stores in Old Town, Estonian Handicraft has stores at Kuninga 1 and Viru 1, Rewill handicraft store is at Vene 7, close to the hat shop and the Katariina Passage (Rewill is the store where they sometimes have the knitted "Isabella of Toledo stockings" of wool and you can order them there).
Food in general is cheaper in Estonia than for example in Finland. As I usually rely on public transport, I tend to be very picky with what I carry home.
I'm a tea drinker, so I often grab some tea (loose or in bags) from a grocery store. For central European visitors this may not pay off except if you like Russian tea. Same thing with herbal drinks: the Estonian selection is a lot wider (and cheaper) than the Finnish mint-rosehip-and-chamomile, so I often bring herbals and/or decaf teas (there's an originally English peach flavoured decaf tea I especially like).
The other favourite I have is the Estonian cakes and (sweet) pastries - I can get two or three to the price of one in Finland, so I often have a box of something sweet when going home from Tallinn. Estonian sweets and chocolates are different from at least the Finnish stuff (more "Russian" in a way), so I usually grab a bag or two of Kalev's produce and some chocolate of theirs.
What Finns mostly ferry over to Finland is of course alcohol, both beer and spirits. Estonians have the German beerbrewing tradition and their selection of beers is very wide from lagers (even weissbier) to strong dubbelbocks. Unfortunately the (to my taste) more interesting sorts tend to be in heavy 0.5 liter glass bottles, so I'm usually very picky with what I take home.
A nice and inexpensive alcoholic gift to somebody at home is to get some of the Estonian berry liquors. There are also interesting berry wines, for example of rowanberry. Several local vodkas exist as well, among others Liviko's Viru Valge and Viru Vägev (stronger one). Herbal liquor Vana Tallinn is also popular as a souvenir.
Nowadays I buy most of the food and drink (all types of alcohol is
sold at grocery stores, no restrictions there) to take home at the the
big Citymarket at the port (near terminal D); it's open 7-22,
i.e. almost always, so it's a good last stop before the ferry. Close
to the port there's also another shopping complex, Merekeskus, where
alcohol is probably cheaper (no food, though) and at the port there's
an another, more touristy type of shop (souvenirs, sweets, alcohol),
Sadamarket. The distillery Liviko
has a store on the way from the town to the port at Mere pst 6, it's
open Mon-Sat 8:30-20:00 and Sundays 8:30-17:00. If you want to see a
good selection of Estonian berry liquors and spirits, this is a good
place to go to. I'm sure Liviko's products and other similar drinks
are available at the tax free at the airport as well!
Note. Do not buy spirits somebody offers you on the street. The bigger shops are a safe choice (they have their big Finnish commerce at stake) and there's never been problems with beer, wine or berry liquors, only the hard stuff bought on black market.
In the center the best selection of all types of food is probably to be found at Kaubamaja at Viru square. It's not the cheapest place around, but easy to find and there really isn't much choice in the center. If you go to the fabric shops Eesti Tekstiil and Kangas ja Nööp at Kadaka tee (away from the center), there's a reasonable (and reasonably priced) Selver supermarket next to Kangas ja Nööp (same building; even the bus stop is called "Selver"). I often grap some "lunch on the fly" from here, i.e. a roll or pastry and a drink and maybe a banana or something similar.
Note. If you have the time, the cafeterias/coffee shops in Tallinn are (by my standards) inexpensive and sell all those wonderful cakes and also soups and other light meals. For example Majasmokk at Pikk 16 is very popular, but pick any you like the look of - all cafés in central Tallinn are quite reasonable (and safe).