In my opinion, the quality of diving is much better in the Philippines and Indonesia, compared to Phuket. All three locations offer plenty of dive operations and are relatively economical to travel.
If you head towards the Philippines, then you should know that there isn't any diving directly in Manila. You can travel to Subic Bay or Anilao (3-4hr bus) or catch a bus/ferry to Puerto Galera to hit the nearest diving spots. Cheap(ish) internal flights will take you to other locations, such as Cebu or Bohol. From Cebu, you can also travel onwards to Moalboal or Malapascua. Different locations in the Philippines have different 'vibes'... so there is plenty of scope to pick a destination that suits your budget and personal preferences.
Here's a breakdown on the primary locations:
Subic Bay - former US Navy base, just north of Manila. Easily accessable by bus (cost approx 225php each way/trip 3-4 hours). It is a very sheltered bay, offering reliable diving in anything other than the most severe weather conditions. It is world reknown for the large number of diveable shipwrecks, including many WWII American and Japanese warships. There are also some pleasant coral reefs with a wide variety of marine creatures. The variety of shipwrecks makes this an excellent destination for history buffs and technical divers. The calm water conditions and shallow water make it perfect for training courses. Water visibility at some of the sites can be lower, due to silting from the river that feeds into the Bay (a problem that has persisted since the eruption of Mt Pinatubo in 1991). Plenty of hotels and resorts to suit most budgets. Not all resorts have a nice beach.
Anilao - A quiet province, just south of Manila. Accommodation is almost exclusively in isolated resorts, which means that transport is not as direct. Many visitors opt to hire a driver/car or taxi, rather than go on a multi-stage trip using public transport (typically bus to Batangas, Jeepney to the nearest town, then trike to the resort). Car/Driver/Taxi will cost in the region of $100US. Very secluded locations, lots of peace and quiet. No nightlife outside of the resort. Beaches are mostly pebble, not sand. The area is known as one of the best 'macro' marine life locations in the world, with very high bio-diversity. This is a great place to dive, if you have an interest in brightly colored nudibranch (sea slugs), exotic shrimps, crabs, eels and octopus. There are, of course, many fish species and occasional encounters with pelagic animals like sharks and mantas. The variety of marine life and macro critters make this an amazing destination for underwater photographers.
Malapascua A little off the beaten path, this island has a sleepy and secluded atmosphere. It is accessable via flight to Cebu, bus/taxi to the northern shore, then water taxi. The island is world famous as one of the only locations where divers can reliably encounter Thresher sharks. It is also reliable for other pelagic encounters, such as manta rays. It has a wide bio-diversity, with much macro marine life and schooling fish. I recommend Evolution Divers. Matt (one of the owners) is here on SB.
Moalboal A few hours south of Cebu, this is another top Philippines diving destination. It is famed for it massive congregations of schooling fish. Again, not much infrastructure or commercialization here. Check out Savedra Dive Centre.
Coron On the island of Palawan, accessable by internal flight. Coron is another world famous wreck diving destination, with many Japanese war wrecks. Lots of nice resorts around the area. Can trip from here to visit the 'Underground River' near Puerto Princessa. This is well worth the trip and is in competition for recognition as one of the new 'Seven Wonders of the World'. It's also a UNESCO World Heritage site.
Bohol An island next to Cebu. It is accessable via direct flight from Manila, or via ferry from Cebu. Good all-round diving, nice coral reefs. Plenty of interesting non-diving activities, such as the 'Chocolate Hills' (UNESCO world heritage site) and seeing the 'Tarsier monkeys'.
Phuket, Thailand, is a much more commercialized holiday location than anywhere you'll find in the Philippines. There are a wide variety of dive centres and several members of this forum work/own centres there. IMHO, the quality of diving there isn't as high, unless you spend more money and opt for a liveaboard trip that reaches some of the offshore sites not accessable by day boats.