Cocoa Beach is far closer to WDW than Daytona. It's also a lot quieter. Just take 528 east (a toll road), also called the Beachline (or "Beeline" previously), and then get on A1A going south. It'll take about 45-60 minutes to get there depending on traffic and your starting point in Orlando. I've found that unless there is a space launch that 528 is a relatively uncrowded road, even during rush hours.
If you want to get away from some of the more touristy stuff like Ron Jon, the big hotels, etc. go a little further south on A1A and park at one of the beach access lots on the "South" named streets, such as 4th Street South, etc. You'll actually pass a "Welcome to Cocoa Beach" sign and "downtown" Cocoa Beach en route. The beach is just as nice there, but there are far fewer people (and businesses) along that stretch. This adds 5-10 minutes to the drive, but is well worth it, IMHO.
