I've only dove off Cocoa once and it was during lobster season. If you can find a dive boat, there are some pretty decent areas to explore off shore. As far as beach diving goes, my advice is to get a copy of Diving Guide to Underwater Florida. There's some decent shores dives a little South of Sebastian, around Vero Beach.
I'd agree with the previous post and West Palm is going to be the prettiest area or maybe check out Jupiter. It's generally a little deeper dives and shorter of a drive.
Once you check out the book you'll get a better idea of places to explore. Also, Blue Springs in Orange City(near Orlando) is worth a dive. Need to be Cavern certified to have a light, but it's a nice place to rinse the salt off your gear.
HTH, Robert.