We went a few weeks ago to Sand Key. (I think!) I had heard reviews re: the beach at the Holiday Inn there, but decided to hop over to the private park beach and it was fabulous! There were only 3 people anywhere remotely near us! And, the beach was nice, lots of shells, found huge ones in the water! My 2yo dd even loved it (for a change!), since there weren't many waves. She practically stayed with me in the water the entire day.
At this park, there was metered parking, and a nice changing area.
Sorry I can't remember the exact name, but I was indecided as to which beach we were going to that day, and that's just where we ended up!