Chiang Mai is the place for Thai handicraft, almost everything you will find in the country is produced in the region. So it might be a good idea to do your shopping in Chiang Mai, you'll have the choice and you should get the best prices, but it's really up to your bargaining skills.

Local handicraft doesn't mean cheap souvenir like rattan ashtray or paper lamps that will end up in the bottom drawer of your cabinet, there are some very good quality stuff produced by skillfull and creative craftmen, in fact real artists.

If you express your interest for local handicraft, there is a 99,9% probability you will be offered a tour to the Sankampaeng road (the 0,1 missing percent means the person you're talking to is deaf). The sankampaeng road stretches for kilometers between Chiang Mai and ... Sankampaeng. All kind of Factories and showrooms have been built there, waiting for you.
Wait, there is a small problem here, how come when i buy something from a so called factory, i have to pay more than for the same object at the Night Bazaar ? You may choose to believe the sales person who will tell you it's not exactly the same product, that the quality is different, but the main reason is that whoever drove you to the place (taxi, bus or tuk-tuk driver) will get a commission on anything you buy. Add to that the fact that it is becoming difficult to bargain in those places (so many buses bring flows of tourists ready to pay the price without question).
In other words you can go to visit this area, it will give you a good idea of all the different kind of products available, just don't buy there or go there on your own (rent a scooter) and don't pay attention the 'fixed prices' signs you'll see, just bargain.

I hear your question... where to buy handicraft then ?

• The first obvious choice is the Night Bazaar. Yes it is the most touristy place around, yes they sell all kind of poor fakes but there is quality too. The Night Bazaar as it is known today refers to a busy street crowded with all kind of stalls selling everything from DVD copies to... rattan ashtrays. But originally the Night Bazaar was the name of a 2 storey building (next to the D2 hotel). The place still exists of course and it is there that you will find the good stuff: Lao silk, unique white celadon, original paintings, delicate silverware, cheap essential oils... to name a few.
• The Sunday Market is great for little handicraft, this market held between the Taphae Gate and the Wat Phra Sing Police station is very popular aomng thais, the atmosphere is relaxed, prices are at their cheapest. You won't find the fake things there. This place is only for local handicraft.
• The Taphae Road and the Loy Kroh Road (also famous for its bars) have some very interesting shops, producing unique items (home decor, fashion, jewelry) it is worth a stroll.
• Luxury handicraft shops are found in the Nimanheimin Road.
• If you want  painted fans or umbrellas, it is all in the Borsang village, on the road to Sankampaeng.
• If you're looking for furnitures, you'll have to go to the Hangdong area, a superhighway starting near the airport. The shops there will also take care of the shipping.
• And if you're into wood products, you definitely must visit the Ban Tawai, a village specialized in this craft. You'll also find very nice reproduction of antique furnitures (many imported from China or Central Asia).

Tip: there are quite a few free magazines distributed monthly in most hotels, shops and restaurants. They include maps and loads of adresses to local shops. Art & Culture Lanna, Passport to Suvannaphoum, Guidelines are 3 good magazines.