Strictly speaking, no, there is no fast travel system in Dying Light: The Beast. You cannot click on any location on the map and teleport to it. Not Safe Zones, not cleared objectives, nothing.
In place of a traditional fast travel mechanic, Dying Light: The Beast offers a few olive branches. The first is the map size. While Castor Woods is certainly a large location, it’s not so big that you can’t simply run to almost anywhere you want to be in more than two or three minutes.
You’ll need to avoid zombies and combat generally to do so, but there was never a time in my review playthrough where anything felt too far away.
The second, newer addition to the series is vehicles. The green Park Ranger and black Baron trucks all do exactly what you’d expect them to do: allow you to travel more quickly from place to place. You will want to stick to roads and other major thoroughfares while in a vehicle, and avoid doing too much damage to it, of course.
So long as you have a relatively straight shot to your destination, driving there is almost always going to be faster than running. If, however, you’re headed into the wilds of Castor Woods, you’re probably better off hoofing it.