If you havn't seen one, an elephant show, then it is a must. We visited a place called Maesa, which is about 20km from Chiang Mai. Only 100bt to enter. Heres the link...
Maesa Elephant Camp : Chiang Mai, Thailand.The show is on at 9-30 and 13-30. In the same valley, a few kms away is a touristy Hill Tribe village, worth a look, but seemed expensive to enter.
Night Bazaar for shopping is great.
A walk around some of the old temples in the centre of the "moat" is worth it, too.