Within Chiang Mai city, it is very easy to get around as the city is very compact. If you are fit and able, I recommend that you rent a bicycle. Go Green and Save the Earth! The rent is just 20 to 50 baht per day, depending on the length of your rental.
You can also rent a motorcycle. Prices range from 100 to 150 baht per day.
Of course, car rentals are available too.
Songtaews are the most convenient public transport. You can flag these pick-ups along any street within the city. Only the red pick-ups can serve within the city. The other coloured pick-ups connects outside the city. Prices start from 20 baht per trip per person.
Tuk-tuks are more expensive than songtaews. Prices start from 60 baht per trip. But if you travel with one buddy or more, you can split the cost. So it may be better for your group to take a tuk-tuk as it’ll be faster than a songtaew (tuk-tuks go direct to your destination while songtaews will pick up and drop off passengers along the way).
Air-conditioned taxis are quite hard to find inside the city. They usually hang around the Central Airport Plaza or near the tourist spots.
You may have seen one running around the city: the Chiang Mai public bus. Yes, it exists! But it is hard to find out the routes they run. Due to low public demand, many of the routes have been stopped. Some of the bus shelters you see in town are not being served anymore. So if you have been waiting for the bus for more than 10 min, better try other types of transport!