First of all, looking for a place to visit in the Philippines is quite a big question. But since you will be arriving via Manila, best to visit Intramuros that holds a lot of information about Philippines - Spanish history.
For Cebu - Bohol, either you take plane or hop in ferry boat. I think pau_p1 pretty summarized what you can expect in those two islands.
If you are into diving, you will definitely love two two more.