Yes there is a watersports complex off of I-95 or the turnpike. I've never been and don't know if it is private or not.
I grew up in Stuart just north of Palm Beach and rode there for many years. The best place for calm, mostly fresh water is in the South Fork near Palm City. There is a boat ramp at Leighton park that will drop you close, and you head south through the no wake zone for about 15 minutes. Where the slow zone ends is a big island. This is the spot. The more zoomed in map shows the island with the words "St. Lucie River" on the northeast side. The river is wide enough to drive double ups at both the north and south ends of the island.
Before you head up there I would try to check the status of the slow zones, since I haven't rode there in quite a while and its possible FWC made the entire area no wake. It looks to me like there is a boat moving at a decent pace on the satellite, so you should be fine.