The Dead Sea is in a major crisis, with ever more sink holes emerging and beaches being closed as a result. The water line shifts (i.e. reduces) by several metres every year, and you can see the old beach structures from the 80s several kilometres from the shore line!
The Dead Sea shore is 'managed' by Israel, and sadly there is no escaping the israeli tourists that come for the day from Jerusalem or Tel-Aviv. Luckily at least Palestinians have access to the northern part of the sea, with cooler water (still luke warm) and more of the famous mud, which people rub over their body and let soak / dry for 30 or so minutes.
Kalia beach is a safe bet. Entry is around 50NIS and they have bars and a nice picnic area as well. For Palestinians it is best to have a group of both males and females arrive in the car. All male groups may be rejected.
Kalia is open from 8am - 5pm every day. (at least I didn't find any evidence of the contrary).