Cocoa Beach is about an hour east...true ocean type beaches there, with a fair amount of stuff to do. We stayed at a Doubletree right on the beach in Cocoa Beach a few years ago..it was quite wonderful.
Or, if you head west, you're about 90 mins from the gulf. My ds lives in Tampa and it's wonderful to spend time with him at the beach. We always go to Ft Desoto, but that's another 30 min drive from Tampa itself. The drive from WDW to Tampa is about 70-75 mins, then another 30 to the beaches. St Petersburg is beautiful as well.
If you head west, you can always leave from Tampa International if you are flying out. Very nice airport!!!