mackm - I also fish out of Port Canaveral. Lots of great places (inshore & offshore) to fish around here.
If you want to do some offshore fishing w/o chartering, then you could try the Ocean Obsession - here's a link for you:
http://www.fishobsession.com/65oceanobsession.php
If you want to charter up to 35 miles offshore, then here are a few that you could try:
http://www.coolbeanscharters.com/
http://www.thebottomlinecharters.com/
http://www.fishrelentless.com/trips.html
http://www.bottomdollarcharterfishing.com/pages/918946/index.htm
Here's a link to many other charter boats for the PC area:
http://www.fishingspacecoast.org/Boats.html
If you want to fish for Tuna on The Otherside (70+ miles), then you could try the following:
http://www.aasportfishing.com/
http://www.ticketfishing.com/
For inshore fishing (Redfish, Speckled Trout, etc.), you could try Sebastian inlet, Mosquito Lagoon, all along (numerous parks, etc.) the Indian River, etc. You can drive up to most of these places and just throw out a line. Be sure to stop by a local tackle shop, Walmart, etc. and pick up an out-of-state temporary fishing license - I believe they are around $10.
There is also a nice pier at Jetty Park that you can fish from. Here's a link to some information about the park:
http://www.portcanaveral.org/funport/parks.htm
Enjoy the area!
Disclaimer - I have no relationship with any of the boats, captains, parks, etc. that I have provided links for. In addition, I have never fished on any of the boats or with any of the captains that I have mentioned in my response.