Chiang Mai is actually an ancient city. The old city of Chiang Mai is surrounded by wall of red bricks and a moat. I took the effort to walk and find one of the historical gates - which was very near to the Saturday market.
Here, visitors could see the remaining wall which was built many centuries ago. There are actually many other gates around but I was too lazy to walk and explore (and due to time constraint).
The place near the gate was quite busy late in the evening when I was there. Besides the Saturday night market, there were also food stalls along the moat by the roadside, which could be another attraction of the place.