The obvious things are the mountain temple and the walled old city; the less obvious ones are a contemporary art museum out in San Kamphaeng and an elephant sanctuary where nobody rides anything.
Wat Phra That Doi Suthep
The late-14th-century hilltop temple about 15 km from the city, visible clinging to the mountainside from the plain below and reached by shared songthaew from Chang Phueak Gate. The complex also houses the temple's International Buddhism Center, which runs Vipassana meditation courses with accommodation for foreign visitors.
Elephant Nature Park
A rescue sanctuary in a valley north of the city with no riding and no shows; half-day visits are 2,500 baht, most full-day programmes 3,500 baht, and an overnight is 5,800 baht, with children 3–11 at half price. Booking and pick-up are handled from the office at 1 Ratmakka Road in Phra Sing.
MAIIAM Contemporary Art Museum
A private contemporary art museum at 122 Moo 7 Tonpao in San Kamphaeng, about half an hour east of the old city, open Friday to Monday 10:00–18:00. It holds the Bunnag and Beurdeley families' thirty-year collection and shows serious Thai and Southeast Asian work; check its social feeds for the current ticket price.
Chiang Mai National Museum
The Fine Arts Department museum on the Chiang Mai–Lampang superhighway in Chang Phueak, with the exhibition building open Wednesday to Sunday 09:00–16:00. It is the clearest single explanation of Lanna history you will get before wandering the temples; phone 053 221 308 to confirm before travelling out.
The old city temples on foot
Everything inside the square moat is walkable in a morning: Wat Chedi Luang's ruined brick stupa in the centre, Wat Phra Singh at the west end and Wat Chiang Man, the city's oldest, in the north-east corner. The larger ones charge foreign visitors a small entrance fee; cover shoulders and knees and go before the heat.