Just as an FYI, Daytona and Cocoa Beach are every bit of an hour from each other.
From Cocoa Beach, the fastest route is down I-95, it's about a 3 1/2 hour drive. If you take Route 1 it's more scenic (but not right on the ocean like A1A) but lots of small towns and traffic lights, and speed traps. Plan on about double the time on Route 1, maybe even more on A1A.