Well, for first time visitors and given the stuff you wanna do, I guess, the Visayas and Palawan will be alright. You can also add in some days in North Luzon. It's also relatively safe in those areas.
You can go Surfing in Siargao (Northern Mindanao, near the Visayan island of Leyte), Diving (throughout the Visayas), Swimming with Whale Sharks (Either Donsol or Oslob, but the latter has poor reputation), Hiking/Beautiful places/Relaxing/Hanging Out (pretty much everywhere in Visayas and Palawan).
May I suggest the following itinerary:
WEEK 1 (Culture+Highlands): Manila (Intramuros, Makati, Mall of Asia) plus North Luzon (Banaue, Sagada, Batad) OR Central Luzon
Spend at least 1-2 days in Manila then the rest of the week at North Luzon. You can fly from North Luzon to the Visayas (Cebu) via Angeles City. A caveat: do not skip going to at least one mall. It's part of Filipino culture already, and you'll see a microcosm of Philippine society there. Recommended ones are Mall of Asia (for it's size)and Greenhills (cheap clothing, bags, etc.)
WEEK 2 (Beaches): Either Western Visayas (Boracay-Iloilo) OR Central Visayas (Cebu City, Malapascua, Oslob, Panglao, Chocolate Hills) OR Pacific Seaboard route (Daet, Naga, Caramoan, Mayon Volcano, Donsol > Biri Island > Siargao)
The Pacific Seaboard route is significantly less touristy than the first two. Admittedly, you'll need a more adventurous (or hectic?) pace since it covers much more areas than Western/Central Visayas, but the variety of landscape is definitely rewarding - you got beaches, snorkelling, diving, volcanoes, etc.) As for the usual destination places of Boracay and Cebu, the pace is leisurely, and you're bound to meet fellow tourists there.
WEEK 3 (Diving/Snorkelling/Landscape): 4-5 days in Palawan (El Nido, Coron), then spare 2-3 days for Around Manila (Tagaytay, Corregidor)
