I will preface my post by stating that I live on the West Coast of Florida, near some of the nicest beaches in the world.
But, I recommend that you head East. If the purpose of the trip is to see "the ocean," then you want to go East and see the Atlantic. I would just go to Cocoa Beach, which is only about an hour from WDW. It isn't the nicest beach in the world, but it is a nice beach, and there are plenty of restaurants and other things to do there. There are also plenty of places to park, and the traffic won't be bad.
Unfortunately, the drive West to the beach is likely to take you twice as long, because of traffic once you hit Tampa. Clearwater Beach is a wonderful place, but the parking and traffic are horrendous.
Honeymoon Island and Caladesi Island State Parks are both very close to where I live, and I would very much recommend them as places to visit, but I wouldn't recommend them as being a convenient drive from WDW.
TCD