As this forum is not real busy I will try to help. Its a very low key area. Not as busy as the Amelia Island area. I know there are a few restaurants beachside nowadays. The Things to Do list above includes a childrens museum. Nearby Stuart also has some restaurants on the Indian River Lagoon. They used to have a big flea market over there, not sure if the still do. You could probably find a canoe / kayak trip in the area. Nearby In West Palm Beach you have Lion Country Safari which is good for about 1/2 day. Older park with a water play area if the kids are young enough for that. Not anything like a Disney park but interesting.
In Winter months manatees hang around the power plant, not sure if you would see any at this time of year. Nearby Jupiter has the Blowing Rocks which if you make the trip to Lion Country you could see on the way (check times for high tides for best results). The Dive Bar on Jupiter Island has really good food.
You might also try posting this on the Port St. Lucie forum.