May Kaidee's is a good place to start. http://www.maykaidee.com/site/cooking-school They have a very long-running cooking school in Bangkok and now in Chiang Mai by the looks of things.
I had an extra day with nothing to do so I went looking for an affordable cooking class. I went here.
The market visit was to a small market in the Silom area. The classes were hands-on.
I went away satisfied.