Honestly, we went to Puerto Princesa just to experience this!
It's a MASSIVE underground river cave system, designated as a UNESCO World Heritage Site in 1999 and voted as one of the New 7 Wonders of Nature in 2012.
Exploring it is definitely a bucket-list item, so don't skip it during your stay in Puerto Princesa. You can explore the cave via boat on a tour, while seeing the local wildlife and culture as well.
HOW TO GO THERE
It's not possible to visit the Underground River without a tour, as it requires a permit and has specific regulations for access.
Thankfully, there are HEAPS of tour operators available in town! They're quite affordable, too (~40-50USD)
Most tours include pick-up and drop-off in PPC, lunch, and visits to other spots on the way.
Here's an excellent tour to the Underground River if you're keen!