We prefer the other coast, the waves are nicer. Gulf side is just too calm for our liking, but the sunsets are phenomenal. It's about 2 hours from WDW to Clearwater Beach or St Pete's Beach which are both nice (and there's a whole bunch of beaches in between these 2 like Treasure Island, Indian Rocks Beach, BellAire Beach etc). We found it a little disconcerting that they had signs up warning you to watch your step in the water because it is Stingray Season from April through September.
It's about 80-90 minutes north-east on I-4 to Daytona Beach, which is our favorite, tons of stuff to do, and arguably, one of the best beaches in the USA. And how cool is this: you can drive your car right on the beach.
Cocoa Beach is about 75-85 minutes east from WDW on sr417 and then SR-528 which are toll roads ($5 or $6 each way)