Yes, there is one near community center but the actual two long beach public parks are : one right next to cosmos ( #1) and then yes, farther up near the AI's is #2..there both kept up well and their is an admission fee (cheap-forget how much) I cant rec. the places enough-esp to people who get sick of the BS on the main 7 mile beach..both places have showers, restrooms and wonderful, natural beaches..Nothing fancy but clean...In fact #2 has excellent shower facilities-when my water was off for days I ended up going there everyday to wash up-well worth the cheap admission price.
The one near the community center that has the parties on sunday night is public but not run by the same organization...in fact i dont know who is responsible for that area...