Sava River
Zagreb is flat! The best run I found was along the Sava River. This river divides old and new Zagreb; until the 20th century, not much had been built south of the river. There are dirt paths on both sides of the river and the path goes for quite a distance. The main drawback is that the river is 1-2 km from the Lower Town (and further from the Upper Town). So you have to run on city streets to get there; in general, there are wide sidewalks and not too many crosswalks. Additionally, drivers in Zagreb are very polite, always giving right of way to pedestrians where there was no traffic signal.
Maksimir Park
Maksimir Park is the largest park in old Zagreb. It's located east of the Upper/Lower Town. From Jelacic Square, it's about 3 km away on city streets. If you don't want to run to Maksimir Park, you can take either the 11 (towards Dubec) or 12 (towards Dubrava) tram from Jelacic Square to the Park Maksimir stop (or google map public transit directions from your location).