We visited Palawan in the second week of January and stayed in Astoria Palawan. Here's our itinerary:

Day 1
12:30 PM Arrival at Puerto Princesa Airport
2:00 PM Arrival at Astoria Palawan
4:00 PM Check-in

Day 2
Puerto Princesa Subterranean River National Park Tour

Day 3
Puerto Princesa City Tour
- Immaculate Concepcion Cathedral
- Baywalk
- Palawan Butterfly Ecological Garden and Tribal Village
- Baker's Hill
- Ka Joel's Restaurant

Palawan Waterpark by Astoria

Day 4
Port Barton Island Hopping