CEBU
This is the 2nd major airport hub in the Philippines next to Manila. I hour by plane from Manila. It is also international so you can come in from Hongkong or Tokyo Narita. The airport is situated on Mactan Island which is around 20 minutes to Cebu depending on traffic. It is also the next major hub for inter island vessels and the port is in Cebu City. Major hotels are in Cebu City like the Marriot and Marco Polo (they might open when you get there). There are also smaller hotels. In the city, you can visit Magellans cross (replica) and the Sto. Nino (child Jesus) which they celebrate in commemoration of the conversion of the pagans to Catholicism in January (Sinulog). I am not sure what day it is so you better reserve hotel and plane soonest.
Then there is Mactan Island where most of the beach resorts are like the Shangri la, Maribago Blue Water, Tambuli East and West, Cebu Beach Club, Costabella to name a few. The more accessible dive sites are the Tambuli fish feeding area (plane wreck), the Marigondon cave (very advance diving unless you have a good guide), Shangri la. Not so much fish in the area but worth a dive. Then you have Hilutungan and Nalusuan which is around 30 minutes by banca from the coast of Mactan if you are staying in the resorts I mentioned.
Bohol
Tagbilaran is the capital and this is where airport and port is. By fast craft it is 1 hour and 30 minutes. By plane from Manila is around 1 hour and 20. Phil. Airlines or Cebu Pacific. There are hotels in Tagbilaran. I can get a good guide for you to see the Tarsiers, Chocolate hills, have meals in ancestral houses, visit the oldest stone church in the Philippines, do river cruises in Loboc and Inabangga (2 hours away), do camping. I am afraid two days is not enough in Bohol. Wednesday is market day in Antiquerra. Lots of arts and crafts. Eat lots of seafood.
The resorts are found in Panglao Island. 30 minutes from Tagbilaran. Bohol Beach Club (2km white beach), Ananyana, Alona Beach (lots of resorts run by foreign and locals). All of them have dive shops and the rates are usually the same. US$30 per dive around. Dive sites are Balicasag Island, Cervera Shoals, Pamilacan Island (Whale Museum), Duljo Point.
Negros Oriental
Dumaguete is the capital. Airport and port is found here. Flights from Manila. Slow boat ferry from Cebu side like Naga, Santander. You can take your car on board or take the Ceres bus line which is around 6 hours or could be more. I am not sure if fast crafts are still running Tagbilaran to Dumaguete or Cebu Dumaguete. Usually is 2 hours trip.
Friday night the boulevard turns into a festival of students (Dumaguete is University town) and they are all riding their motorcycles (you can rent) and turning the boulevard into a big bar. Lots of good eating places and bars. Siliman University is run by Presbitarian (I think) so there are a lot of Americans or foreigners studying in Dumaguete.
Check out the Siliman Marine Lab and Museum (if they are open). Whale bone and stuff. This was where the first study of Marine Mammals was made in the Philippines. Old colonial architecture.
Hotels in the city like Bethel. Lots of small hostels by the boulevard. Resorts are mostly in Dauin which is around 11 kms away and about 30 minutes. El Dorado, Atlantis and Bahura Resort (run by Scubaworld). All have dive shops. Dives are around US$ 30 or even more if you are diving in Apo Island. This is the best diving which is around 40 minutes by banca from the resorts. The house reefs of the resorts and the Dauin reefs are great for Macro. Seahorses, stargarzers, nudi, etc. You have to try Masaplod Norte. Small reef and shallow but lots of fish although vis might be bad especially this time of the year because of the north easterly winds and crossing to Apo Island.
Wednesday is market day in Malatapay which is next town to Dauin.
Hope this helps.