The Underground River is an easy day trip from Puerto Princesa city, Palawan Island. There is a limit of just under 1000 on the number of visitors per day. I went before this was implemented, but it appears hotels and B & bs are able to easily source 'tickets.'
Philippine Airlines has just resumed nonstop flights to Kuala Lumpur from Manila, and from memory Malaysia Airlines also operate that route. There are quite a few flights from Cebu down to Singapore and Cebu is highly recommended as a stress free airport (it's on an island called Mactan) to get into or out of Philippines.