I was there about a few years ago. I had my itinerary planned for me so I can't remember the places I went (thai names are quite a handful )
The mall had a pretty good cinema but the prices in the shops tend to be comparable to SG. The night market was pretty much where I went. I recall going to more than 2 around the city. They were exceptionally crowded. Carry S$100 cash, a camera, a bag for shopping and nothing else and you shouldn't worry about losing anything to thieves.
Doi Inthanon is a fantastic location that you MUST visit. The buildings at the peak was under renovation when I was there, but it was still a memorable place. On the surrounding slopes are lush forest trails that were very enjoyable to walk through. Arrange for transportation and spend a day there. Do not give this place a miss!
The rest that I can remember are temples. Just pick one and go. You can't really go wrong with temples. If you want to go somewhere in the morn, the zoo is not bad. There's a place where they cultivate orchids and it's a good place to buy sovenirs, but be prepared to pay tourist prices.
Doi Suthep is the nearest mountain you can visit if Doi inthanon is too far (or expensive) for you. Enjoy sceneries, cool air and many photo taking opportunities. There are also some hill tribes if you like to visit.
Chiang Mai Zoo is famous as there's panda, it's at the base of Doi Suthep.
Some malls for shopping and not forgetting the night bazaar. Tourist prices though. You may also try Ping river cruise if you like to just sit down and relax while they take you on a relax boat ride.
Best time to visit is Nov-Jan, where weather is cool and dry (no rain). In Northern Thailand, Nov is the sunflower bloom period, while Jan/Feb is the Sakura bloom period. You won't find them inside Chiangmai, but when you travel out to places like Mae Ho and Mae Chaem, you can visit the sunflower field. For Sakura, do visit Doi Mae Salong, and Doi Ang Khang.
1) Temples in Chiangmai worth visiting - Wat Chedi Luang, Wat Phrah Singh, and Wat Doi Suthep.
2) Shopping in Chiangmai - Sunday walking street (more than 2km of crazy shopping that will take you at least 3hrs! Also do visit the more commercialised Night Bazaar on other days.
3) Short day trips outside Chiangmai - Rent a car/bike and do the Sameong Loop, can stop by at Mae Sa Valley, Sankampeng, and Bo Sang Umbrella factories. Can also do Doi Inthanon (highest mountain in Thailand), or onto ObLuang Canyon.
4) Overnight trips out of Chiangmai - Visit Golden Triangle (take a boat ride on the Mekong), Mae Sai (border town with cheap stuffs), Doi Tung, Doi Mae Salong, Doi Ang Khang, Doi Phukha, Pai (beautiful town and surroundings), as well as Mae Hong Son (for the long neck Karens).