Things to do

Despite Chiang Mai not being as amazing as backpackers make it out to be, there are lots of fun things you can do, other than temple-hopping. We thought it would a place where we could just walk to hiking trails and pop into nature, but that's not really possible — you need to get yourself there first by joining a tour or renting some sort of transportation. There are many travel agencies with lots of brochures on planned (multi)day trips / tours / activities by various tour operators you can join for 600-2500+ baht, usually including pickup and lunch.
Some examples include cooking class, trekking, elephant-riding, rafting, zip-line, mountain-biking, tubing, Tiger Kingdom, .... you name it! Most tours take you outside of the city since people come to Chiang Mai for nature in Chiang Mai province, not the city. A lot of people also go northwest to Pai ( map ) with AyaService or by motorbike for more nature.

Some travel agencies may charge more for the same tour, so you might want to check tripadvisor's reviews to see what other people paid. Usually, you do not need to pre-book before you arrive — You can usually book a tour for the next day without problems.

Day Trips / Activities
Trekking though mountains to Akha and Lahu villages as well as to waterfalls in the Mae Tang District and Chiang Doa Mountain Range ( map ), an hour and a half drive north of Chiang Mai. The 1500-baht 3-day tour also includes elephant-riding/bathing in addition to bamboo/white-water rafting. You can also opt for the 2-day tour or just a day trip.
An hour (or 2 if you're slow) hiking up the 1676-meter Doi Suthep ( map ) to the amazing Wat Phra That Doi Suthep for a view of the city. Picnic near the waterfall and spend an hour at the temple.
Doi Inthanon ( map ), the highest mountain in Thailand, has some nature trails and waterfalls. If you're taking one of those 1200-baht minibus day trips, don't expect too much other than getting some fresh air. Arrange your own transportation and spend time exploring waterfalls and hiking instead!
Learn how to make (then eat) your favorite Thai dishes by signing up for a full/half day cooking course! There are lots of schools to choose from and they usually cost from 700 to 1000+ baht. Surprisingly fun!
Nong Buak Hard Public Park, located in the southeast corner of the Old City, is a relaxing free green space with lush lawn and beautiful ponds! If you're lucky, you might even catch the locals playing takraw, kick volleyball played with a rattan ball.
New and used English books are sold in the many bookstores inside/near the Old City, from 60-360+ baht. Done reading? Sell them back for half the price! We go to Back Street Books ( map ), just east of the Old City near Boots. The less-busy temples are the perfect place to spend a quiet afternoon reading.
Within the Old City, there are 3 museums ( reviews ) close to one another. Each one costs 90 baht, but you can get a 7-day pass for all 3 for 180 baht. Open Tuesday - Sunday from 8:30 am to 5 pm.
You can take Thai lessons. We Learn Thai (4-week/24-hour lessons for 2400 baht and AUA (6-week/60-hour lessons for 4800 baht) are the few pamphlets I saw advertised around town. There are lots of other schools too, some offering private lessons as well.