To sum up how it all finally turned out:
Ibound flight - Europe - Istanbul - Hong Kong - Manila - Siargao (with layovers in the airports). Siargao is a nice island if you're into surfing. For someone who tried it for the first time ever, I wouldn't say this is a must-go spot, or maybe the weather conditions weren't great. There were not a lot of people around Cloud 9, and it seems the first weeks of December aren't so great to do surfing there.
That being said, I loved the island. Rent a scooter and travel around - the atmosphere is fantastic and the locals are friendly. Not sure if "Rock Pool" is worth visiting - the trip itself was more fun than snorkelling in that area. We stayed in Siargao for 4 days (planned 6) - checked out earlier, and took a flight to Cebu, then a ferry to Panglao. I had hoped Panglao would be nicer, with nice sandy beaches, but it wasn't. I would stay out of Alona beach - went there a few times during the day and night, basically just like any other overcrowded tourist trap. We took a scooter and went to see Chocolate Hills - again, the trip itself was much more remarkable - eating at the local market, talking with the people, trying Halo Halo and having fun. Chocolate Hills isn't that great - but that's just my opinion - I've seen Zion national park in Utah and Great Canyon, Andes mountains, so this one is just a weird shape hills in the horizon.
We got our PADI OWD licenses there, so we spent 3 days with our diving instructors around the sea. Also, took a boat tour - was really worth it, sea turtles, lots of fish, beautiful reef and unhabitated island (Virgin island, if I remember correctly). After finishing PADI course we took a tricycle to Tagbilaran and early morning took off to Palawan, Puerto Princesa. Puerto - a big city, with crazy traffic (so good I didn't risk renting a scooter - would probably give up after 5 minutes). Booked a local tricycle to take us to the firefly tour (don't take any extra packages, like dinner - not worth it), so it's an interesting view and we loved the boat guide. Again, maybe its because of the season, but there weren't many fireflies - only a few spots on the branches. Overall - the view is worth it, but not with the prices that you get in the hotels.
The next day we took a van to El Nido. Absolutely amazing, spectacular place. Spent 2 nights there, also went for a boat tour through the islands (took Tour A). I would recommend to take a scooter and spend a night or two outside - go north to Nacpan, enjoy the more deserted beaches, an evening in a bungalow without electricity and with only a few people around. Perfect chillout. We also went further north to Duli beach - a dutch guy owns a bar and also has a few rooms for rent, also he rents surf boards. Very nice atmosphere there. After that, went back to El Nido, went to the Republica bar to see the sunset (loved it there - the view, the music, the atmosphere). The next day we took a boat to Coron - oh boy, be prepared to get soaking wet, with extreme cold and extreme hot temperatures during the day if you decide to stay on the upper deck (the lower one stinks of gas, but is more or less dry). A trip to remember for sure. The only thing in Coron we did was diving in the ship wrecks (took the whole day). Travelled around with a scooter - not really much to see, the beaches close to town were really poor (if you don't take the boat to bring you to the island), and the further objects, like Baracuda lake, we did not have the time to visit. Afterwards - flight to Manila, a day there and then back home to Europe. Manila - typical big city with its perks (dirt, beggars, shiny shopping malls and traffic jams), I didn't like it but didn't dislike it either.
My personal favorites - Palawan (El Nido and around) and Siargao. I found Bohol a bit disappointing, but a good place for diving. Looking at it now, I would rather go to Siquijor than Panglao.
Weather was fine, it rained a few days for a few hours in Siargao, got some heavier rain in Panglao (but only one day) and light rain in the evening in Puerto Princesa. Other places - warm, sunny / cloudy and nice.
I wanna come back to Philippines, spend even more time in the southern Palawan, maybe visit the volcanoes or rice terraces north of Manila; I would also want to see whale sharks (natural, not the one in Oslob).
Philippines are friendly and we felt quite safe (as opposed to Peru or Bolivia), you can bargain with people but don't push too much and both parties will be happy. The overall happy atmosphere, despite the obvious financial troubles that people have, is something that struck me - people are really optimistic and enjoy life.
For anyone who is thinking whether it's worth going - GO.