To touch upon what others have mentioned:
Dixie Divers (JND SCUBA)
Location: Palm Bay, On Babcock Street in the OutBack SteakHouse Plaza
Major Lines Carried: Dacor, Oceanic, Luxfer cylinders
Agency Represented: PADI
Pool: Off Premises
Nitrox: Partial Pressure Fills
Hatts
Location: Melbourne, at the intersection of Melbourne Ave. and Front Street
Major Lines Carried: ScubaPro, Zeagle, Sherwood, Genesis, Faber Steel and Luxfer Aluminum cylinders
Agency Represented: PADI
Pool: On Premises
Nitrox: Partial Pressure Fills
PDI (Professional Diving Industries)
Location: Melbourne, at intersection of North Harbor City Blvd. (US 1) and Aurora Road.
Major Lines Carried: Aqua Lung, Seaquest, Apeks, Deep See, Atomic, Suunto
Agencies Represented: PADI, NAUI, and TDI
Pool: On Premises
Nitrox: Nitrox produced with DNAx Membrane, banks 6000 cu. ft. of 36%. Offers nitrox blends from 36% on down.
Sea Dragon
Location: Barnes Blvd in Rockledge
Major Lines Carried: Dive Rite, Mares, Atomic
Agencies Represented: PADI
Pool: Currently off premises but an indoor pool is in the works
Nitrox: Nitrox is produced by means of a Nitrox Stick
No dive charters locally, but some good beach diving can be had in the Vero Beach and Ft. Pierce areas during the Summer months. As others have said, closest dive charters are in the Jupiter and West Palm areas (an hour and half to two hour drive south of Melbourne)