I have yet to dive in Panama, but I have been doing a bit of research as I will be there over the XMas holidays and I'm hoping to get a couple of dives in. From what I've read, Panama is not a premiere diving destination, but it does have a few interesting opportunities.
The options available to you depend on the amount of time you have. If you are limited in time, you could dive at Taboga Island which is fairly close to the city. Another option is Islas Perlas which is a bit further and also looks interesting. Both these spots are located in the Pacific which apparently does not have the clear visibility that is available on the Carribean side of the isthmus. If you want to dive on the Carribean side (with allegedly better vis), there are apparently a few spots near Portobello.
Panama Divers will be able to help you, but I can't comment on the quality of service. Apparently you could also dive in the Canal, but having seen the water in it, I suspect that visibility is not it's strength, although it would certainly be unique!
One place we would like to try is Isla Coiba which is 3 or 4 hours by car from Panama City. Apparently there is ample marine life which is the main reason we would like to go. I've come across
this dive shop that specializes at Coiba.
We were in Panama in the summer of 2005 and snorkelled near Portobello. It was quite nice and the water was warm enough that we didn't miss our wet suits. I don't know what the water temp is like this time of year.
I'd love to hear back from you if you do end up diving there. Especially regarding the quality of the dive shop and Dive Master. I'm keen on diving in late December or early January, it's been a couple of months since I dove last...
Richard