You don't go to the Yucatan coast and expect Flagstaff-style running trails, but we are always running on vacations, and it's nice to have an idea of your options when headed to a new place. I could find much on Puerto Morelos / Tulum before I left, so here's a little information about where I ran down there in case you ever find yourself there.
We stayed about 7-8K north of the coastal town on a dead-end road (red star on the map below), so the options were limited to out and backs. The first road that cuts inland (to the Croco Cun Zoo) was busy and didn't have a shoulder, so I never ran there. Instead I would typically wander south towards Puerto Morelos through a mix of residences and the perimeter of a couple all-inclusive megaresorts. Once you hit the town there are more options. You can head inland on Calle Jose Maria, which has a bike path / sidewalk. Or you can keep heading further south (satellite map below). The yellow star is the Grand Residences - once you hit that area, you can easily access a dirt/sand road that runs along the ocean. This was my favorite run of the trip.
Some photos from the "yellow arrows" area...
Tulum is a slightly bigger town and has more roads. The green line I put on the map below is a dedicated bike path, which was really nice. You can make a nice 7 mile loop by connecting the "triangle" of the bike path with the Tulum ruins area. The beach road heading south from the ruins is very quiet and doesn't have any traffic in the mornings.
If you get there early enough (before the tourist crowds pick up), the ruins at Coba would be a great place for a short run. The trails are wide, flat, and lined with trees for shade. Andrea couldn't resist a little jogging while we were there...