Where on Palm Beach? There is MoomBa Beach between the Holiday Inn and Marriott Surf Club.
Another suggestion...
I would suggest having the taxi drop you off at the walkway which is the entrance to De Palm Pier. It is located between the Riu and Radisson Resorts.
Once you reach the end of the walkway at the beach just a short ways to the right you will see the vendors, Itito and New Kid. They rent everything right there: chaises, umbrellas and floats. They also handle all types of watersports. All of the beaches in Aruba are public, but the Radisson's waitresses the last time we were there, were serving drinks and food to cruise ship passengers renting the chaises from the vendors, as well as hotel guests. You could of course walk to any of the restaurants or bars along Palm beach for some "refreshment".
Bugaloe Bar & Grill is at the end of De Palm Pier and is a bit more affordable than the drinks and food at the Radisson. The Riu on the other side is all inclusive so no eating or drinking options there.
The 2 squares you see to the right of the pier itself in this aerial, are the actual tents used by the vendors mentioned above.
There is a restroom behind the Radisson's beachside restaurant, Gilligans. It is towards the opposite end of the beach from where you would be set up with the vendors.