Port Canaveral has no less than 6 very good, safe off-port parking lots (with shuttles)! You can hardly go wrong with any of them and will find many positive reviews as well as the occasional complaint!
The new kids on the block are portparkingspace and Port Canaveral Parking - both with tarmac spots and shaded options. This map shows portparkingspace is closest and really nice but since Carnival docks on the other side of the Port (5 or 6), GoPort, Port Canaveral Parking and Park 'n Cruise are in the direction of Orlando.