What is the best way to get around without being with crowded tourists?
The red trucks, of course. Available all over and for 30 baht or less per person to just about anywhere in the main tourist corridor.
I'd say your best option are tuk tuks. That's the most popular way. Be sure to agree on a price before getting in one! And bargain!
Really the best choice in my opinion is to rent a scooter for only about 150-200baht per day. Riding in Chiang Mai isn't bad -- of course be careful and always wear your helmet. It's much more convenient then grabbing tuks-tuks and red taxis.
Tuk tuk is the best choice. You should choose a stay in the center to get around easily. My friend recommended a good route for me to fully explore Chiang Mai. You can view it for suggestion: https://www.justgola.com/plan/a-wonderful-trip-to-chiang-mai-16553