You have 3 somewhat distinct and different areas to dive in Puerto Rico.
Fajardo area with their trips to Culebra, Vieques and reefs nearby. Probably a good idea, they cater to all kinds of divers. Sea Ventures comes to mind. NE winds in December, swell may be an issue.
Rincon/Aguadilla area. That's where Desecheo trips usually originate from. They are extremely weather/swell dependent, not even a slightest chance for it in December. Few ops offer shore dives, but swell is kinda messing things up with a lack of visibility. Aquatica, Rincon Divers and Taino comes to mind. Wouldn't go there in December.
And here's SW corner of Puerto Rico, Parguera and Guanica in particular. Great option for December trip, but pretty much exclusively boat dives. Paradise in Parguera, Island Scuba in Guanica. But IMHO your best bet with beginners/new divers is Copamarina resort and Scuba Dogs - their shop is in that resort and you can get discounts for booking both together.