As said above, Puerto Galera (from Manila) or Malapascua (from Cebu) are your easiest, best options for good diving. Also as said above, with only a few days available, don't waste a day in transit: choose one place and stay there for all your diving.
PG is easier to get to. Malapascua has more diverse types of dives available. I like them both a lot.
If I had to choose between PG and Malapascua, I would go with Malapascua for the diversity. PG has great reefs, great macro critters, etc but you prob'ly won't see sharks or other big animals, except for a turtle or two. Malapascua's reefs aren'r as good IMO but the macro critters are just as good, plus thresher sharks and white-tip reef sharks; maybe a big ray or two. Couple of good wrecks, too.
Might lose a diving day getting to/from Malapascua, though -- you should look into transportation, and that might tip the scales in favor of PG rather than Malapascua. That was a decisive factor for me last time, so I went back to Subic Bay for the wrecks and then PG for the reefs
My dive buddy is going to Padre Burgos in Sogod Bay in June and I really wish I could join him
but for a first Phillipines trip, Malapascua and PG are prob'ly your best bets.
Enjoy! and post some photos here.
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