For a city with so many public spaces and monuments, Chiang Mai is rather short on parks, as are most Thai cities. Still, it does have a few nice parks worth mentioning here:
Buak Hart Park
Tucked into the southwest corner of the old city is the only park within the city walls, Suan Buak Hart. The park is fairly sizeable, with a large meandering pond in its middle, surrounded by large expanses of grass. There's a paved path around the perimeter that's good for jogging, and is even marked off every 50 meters, so you can tell how far you've gone.
There are several food stalls near the entrance to the park, as well as a few vendors renting rattan mats for those that want to picnic in the park without getting their clothes dirty. Buak Hart Park can be quite popular in the evenings and on weekends, when local families come to relax and play. On most evenings, you'll find guys playing football or takraw in the large paved area of the park.
The path through Kanchanpisek Park
Just outside the southwest corner of the old city, not far from Buak Hart Park, is the newer Kanchanapisek Park. The park was built to commemorate the 50th anniversary of the King's ascension to the throne. It stretches along Om Muang Road and lies between the road and the old outer ramparts of the city.
While all most people know about is the square inner wall of the old city, there was actually a second, more serpentine wall that curved around the southern and eastern sides of the city. This wall was mostly made of compacted earth, and only a few parts of it can still be seen.
A small stream snakes its way through the park, and there are several ornamental bridges across it. There are also two or three small pavilions, but the entire park is not well maintained. Someone cuts the grass once in a while, but it looks like that's about it. Unlike Buak Hart Park, there are no vendors or food stalls.
However, the less popular nature of the park, along with it's long paved path, makes Kanchanapisek Park a pretty good option if you're looking for a place to jog.