Cebu is known for their lechon but to be quite honest I wasn't super impressed. It was still really tasty, but I actually enjoyed the lechon I got in Manila better.
This was a "Lechon Market" in Carcar which I believe is like the lechon capital of Cebu
Then there's also Oslob where you can swim with whale sharks/butanding. Definitely really cool
And there's Tumalog Falls near Oslob but unfortunately it was closed off when I visited last year so I didn't get to see it. I did go to Aguinid Falls which is a smaller set of water falls that you can climb up and entrance was like $3 USD or something and you get a guide that helps you climb. It was a little crowded when I went though
As for Palawan, you definitely have to see El Nido. I stayed in Puerto Princesa and it was meh. There was the Underground River which was kinda cool and there is some island hopping to do but from what I've seen and heard El Nido is A LOT better.