I would not advise this based on the traffic style - but you could run with the local soccer clubs who run daily on the beach. Check it out when you get there.

I ran in Playa the last time down while on vacation. As mentioned, the best place to run is the sidewalks along the hotel row. I'd avoid the actual city part.

The route is pretty civilized, with considerable tourist foot traffic. The one drawback - throughout the morning, all of the local construction workers will be arriving and using these same sidewalks to travel to their worksites. I didn't have any problems with that, but I'm not female either. That may be something to consider.

There is a golf course which appears lovely for a run. I was actually looking for it, but ran past it without noticing. Signs are posted to prevent non-golfers from being on the course, but I'd bet that if anyone said anything, they'd only ask you to leave. That might be a good option for you too, especially if you run early.

Good luck.