The admission fee is 90 Baht for a non-Thai adult and for 180 Baht, you can enter two other sites - the Lanna Folklife Museum and Chiang Mai Historical Centre. It is a fairly good deal for you to have an overview of the culture and history of the Lanna Kingdom. I completed all three sites within 2.5 hours (each of the sites are fairly small). If you only have time for one museum, I would recommend the Arts and Cultural Centre as it has very good exhibits and explanations.
There are also audio commentaries at some exhibits but some of them can be quite long, so be prepared to linger around to wait for the commentary to end. Unfortunately, some of the audio commentaries were not working.
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