Answer:
It depends on what you're trying to communicate. "Run in the street" describes a runner or jogger trotting within the confines of a public thoroughfare. "Run on the street" means any person, conducting the majority of their life (including passing the night there sleeping on an occasional, if not frequent basis), primarily in open, public places, or those immediately adjoining them. "Run on the street" can also be a description of an automobile, which is operated there rather than "Run on a track, or closed course."