Great diving at places like Pescador Island (off Moalboal), Balicasag Island (off Panglao peninsula on Bohol near Tagbiliran), Malapascua and of course Cabilao. Apo Island. All these places can be reached with two to three hours travel by bus / ferry from Cebu City, and an itinary for these great dive spots is easily "strung" together for two weeks of total dive safari pleasure. Direct flights into Cebu City from Hong Kong on Cathay, also from Singapore (w/ a stop in Davao i think) and of course from Manila.
Real off the beaten track spots are easily added: Southern Leyte, Siguijor, Camiguin are just another couple hours of ferry travel away.
The rainy starts around June, true. Have dived the region twice in July and September, both rainy season and never any issues with rough seas / bad visibility. Generally few divers, very cheap diving (USD 15 a dive w/ own equipment is certainly possible), and lots of good stuff to sea. There's pygmy seahorses, sea snakes, big schools of barracuda and jacks, tresher sharks, whitetips, whalesharks at Leyte, all the small stuff you can care for and much more on these Visayan reefs. Am going back this spring - the possibility to dive as many different really good spots as you can pack in your holiday without being confined to one "town" is unmatched anywhere in Asia, IMHO.
Have been in Sipadan in June too, however and can confirm that diving Sipadan is in a different league of diving. The sheer magnitude of action on Sipadan is unmatched.
For me the point is that I am only willing to spend the money for say 7 days of diving at Sipadan, what am I gonna do the rest of my time on Sabah (having travelled half the world I would be morally obliged to spent at least two weeks in the region). Not that special kind of place once you've climbed the mountain and seen the monkies. And although KK is said to be the party town of Borneo, I found it boring as hell (Kuching on the west end of the island much preferred!) No such problem in the Visayas, you just keep tracking to a new spot and do some more dives - all for the same budget as 5 days Sipadan. To each his own, of course.
Wherever you end up - happy bubbles!