One beautiful place that I found in Puerto Princesa to run is the Ramon Mitra Jr. Sports Complex.
It has a regulation rubberized track which was recently refurbished for use during last year's Palarong Pambansa. This track is comparable or even better to the one at Philsports in Ultra. According to the caretakers, the track is free for use to individuals who just want to get in a bit of training. Although large groups will have to ask permission from the city mayor.
If running on the track is not your style, you can also try running on the roads which lop around the 16 hectare sports complex. To my untrained eye they seem like asphalt and there really isn't that much traffic.
Also swimmers and triathletes rejoice, there is also a 50 Meter pool for use. Though the water color seems to show that the maintenance may leave a bit to be desired.