Last visit to Chiangmai I had a bad taxi experience. I was charged 300 Baht ($9.26) for a ride to the hostel from the airport. The price should have been about 150. So this trip I used a bus, for 20 Baht ($0.62).
To access the bus system and go to Suneta you leave the airport terminal from Gate 1. That is a left turn out of the baggage area all the way to the opposite end of the terminal. Go out the gate and turn left about 150 meters to the bus area. Bus #3 is the one you want and tell the driver to drop you at the Tha Phae Gate. Follow the directions here: http://www.tourguizhou.com/chiangmai-suneta-hostel/