If you want an east coast Atlantic beach in South Florida, Hollywood is one of the best as it has a nice couple mile long pedestrian/bicycle boardwalk lined with restaurants. Ft. Lauderdale has unfortunately suffered a lot of erosion so the beach front stretch is not as wide. South beach is nice but much more overpriced. It would require a 3 hour drive to get to
Lego land from south Florida. Daytona and St. Augustine also have beautiful beaches and I believe you can still drive your vehicle right on the beach. The waves do get a little more rough the higher up you go in the state starting around Vero beach area. They are also a bit more natural with more chance of no-seeums which will bite and give you itching welts.
On the west coast St. Petersburg area beaches are nice along the gulf of Mexico and it would put you a lot closer to Lego Land and nearby Tampa has a lot of fun things to offer too, including Busch Gardens.