Apart from the famous weekend markets in Chiang Mai, I recommend a souvenir shop & cafe complex located opposite the Maya Shopping Center in the Nimman area.
Super cute designs, and the prices are affordable too. A shoulder shopping bag is only 250 Thai Baht, and you'll fall in love with every postcard on the wall. Plus, there are many free stamps you can use to decorate your postcards.
Just search for 'PLAYWORKS SHOP&CAFE' on your mobile map app, and it's easy to find.