The answer can be found at the McLarty Treasure Museum (located at Sebastian Inlet State Park). It doesn’t cost a fortune at only $2 a person and under 6s are free. It’s basically one large room of displays and information with a smaller room with a looped video that you can watch too. The video really brings it to life and I’d suggest watching that first especially with children in tow.
In 1715 a Spanish treasure fleet returning from the New World to Spain ran into difficulties off the coast of Florida. At two in the morning on Wednesday, July 31, 1715, seven days after departing from Havana, Cuba, eleven of the twelve ships of this fleet were lost in a hurricane not far from present-day Vero Beach, Florida. Because the fleet was carrying silver, it is also known as the 1715 Plate Fleet (plata being the Spanish word for silver). Over the years a lot of artifacts and coins have been discovered close to the shore. In fact, some local divers have made quite a bit of money recovering items from the lost cargo. The video, in the museum, tells the story in a lot more detail giving the historical background, details of the initial salvage operation and modern day treasure hunts.
From the museum you can walk along the boardwalk to see views of the ocean and take a turn at the pirate ship wheel. After hearing about the riches to be found, I expect children will be keen to go treasure hunting so build in some beach time for treasure hunting. Consider arming yourself with a few low value coins to hide to encourage your treasure seekers.