Hi Corvair,
I reckon the nearest beach (in driving time) to WDW is Clearwater Beach, across Tampa Bay.
Our villa at Hampton Lakes is right in the middle of Florida between the two coasts. But we prefer the Gulf - its warmer!!
Just get on I4 and head south for Tampa, change to US 275, then SR 60 past Tampa Airport and just keep on going.
90 minutes will get you there on that beautiful white sand. I only wish I didn't have to wait until the end of June to be there myself!!!!!