There used to be an ace one the other side of Jebel Ali, but this has now been ruined by the locals moving in and building barasti buildings all over it complete with generators, portable showers and satellite dishes...
You have to go all the way to Ajman and beyond to find a nice beach on the Arabian Gulf side.
There are some nice beaches in Dibba on the Indian Ocean side that are public and easy to reach.
DK, That beach the other side of Jebel Ali has been completely taken up by the Waterfront Development. There is no beach access from Jebel Ali to the Abu Dhabi border.