Chiang Mai is good for shopping. Central Festival, Maya and Promenada are three relatively new shopping centers. They are great for shopping but also include cinemas, coffee shops, restaurants, supermarkets, food courts and other entertainment. Central Airport and Central Huey Kaew also have a cinema. Especially in weekends all these places can be quite busy.
For food stuff the three Rimping supermarkets are excellent places to go. They are not cheap but have a lot of choice and a wide range of fresh fruits and vegetables.
If you need plants, flowers or trees for your garden or fruit tree saplings for your orchard, a good place to go is the plant market, near Tesco Lotus.