Chiang Mai is the cultural center of Thailand in many peoples minds, in fact many of the so called Thai customs are really Lanna cultural activities that have been absorbed into mordern day Thai culture due to their beauty and general fun nature.

You should not miss the Chiang mai national museum or for the avid stamp collector there is a stamp and post office museum  and of course the coin museum or even Bug museum. But it will not teach you much about Chiang Mai culture. 

Truly the culture of Chiang mai is not in the museums but in the people. For Chiang mai is a living culture still very much alive, and the people are what the culture is made of, so visit them in their markets and experience the culture as it really is. Not as a guide thinks you want to see it. One of the best parts about Chiang Mai culture is they are friendly and accepting. They invite you to partake in most any activities they are doing from weddings, to parties, to funerals you are almost always welcome as long as you act respectfully and politely.