It depends how far you want to travel. You have Gulf beaches in St. Petersburg/Clearwater area west of Orlando, and Atlantic beaches in Daytona/Ormond Beach/Cocoa Beach east. You would have 1-2 hr. drive depending on which area you went to. You could do a day trip or an overnight/weekend visit.
Atlantic side will have more waves; Gulf will be calmer. I have always had a fondness for Daytona, but it is not upscale, more funky-tacky Florida beach town.
We've been to Miami before but would like to do the Disney thing with the kids before they're too old for it! I don't want to spend all holiday at theme parks so just wondered what the beaches are like please?