The best diving in Panama is Isla Coiba. It will take a day to get there from Panama City, but it's well worth it. January and February are when you can usually see whale sharks and mobula in the area. You'll also see lots of reef sharks (black and white tipped), turtles, large frogfish, a variety of moray eels and huge schools of jacks and barracuda. The main operators there are Scuba Coiba and Coiba Dive Center.
Isla Coiba was a penal colony for many years, and was not a safe place to visit until 2002 when the penitentiary was closed and it became a national park and marine preserve. It's still very pristine, and has a number of animal species that are only found on the island, such as a white-faced howler monkey. Staying over night there has been very basic, in a few dormitory cabins at the ranger station with electricity supplied only at night. ANAM, the park service, is currently renovating the cabins, so the dive ops are lodging their guests nearby.
Other diving options in Panama are Bocas del Toro and Portobelo. Both are on the Caribbean. This time of year, diving is fairly shallow -- max depth around 60 ft. -- and mainly in the 15' to 40' range in Bocas del Toro and 30' to 60' in Portobelo. Both have limited visibility most of the time. 40' ' 50' is considered a good day. Bocas had more species of coral than anywhere else in the Caribbean, but the shallower corals have been severely affected by warming water and tourists who think it's good to stand on when snorkeling, or break some off and take it home. Bocas has more than 20 dive sites. La Buga is probably the best dive shop there.
Portobelo is the closest dive location to Panama City. You can drive there from the city in about 90 minutes. I haven't dived with them, but two of my Panamanian friends have, and they get great reviews on TA. I would avoid Scubapanama and Panama Divers. They tend to nickel-dime you to death. They start with a very high two-tank dive rate of $130 and then add on a rental fee for each tank and two additional fees for the boat skipper and the DM that are split among the divers on the boat. If you're the only diver, you pay it all. Portobelo usually has only four dive sites for most of the year. That more than doubles between September and November when the seas are calm enough to allow diving on the barrier reef. (The same is true for Bocas del Toro.) That's when diving is really good on the Caribbean side. You see larger animals, more dramatic coral formations and deeper dives.
I don't know of any dive shop in Panama that supports either rebreathers or tech diving. There are only a couple that offer EAN.
