Go island-hopping in Palawan, the Philippines. With a dazzling array of activities and safety protocols in place, this leafy archipelago could be a good option for a “new normal” getaway.

The museum, which opened in 2011, was created by Higinio “Buddy” Clark Mendoza, son of a former Palawan war veteran. A helmet and flagpole near the entrance honors the “Palawan Fighting ...