All beaches in Aruba are public. There are any number of nice beaches. All are accessable by cab or even by the very reliable buses (terminal is right opposite the cruise piers).
The nicest , widest beach is Palm Beach. This is the area by what they call the "highrise" hotels. Head out for the area somewhere between the Aruba Grand and the Holiday Inn hotels. Beach is great and there are three piers run by various tour companies (Pelican, Red Sail and DePalm) that have food, bars and restrooms. In addition to these three major tour companies (offering sailing , snorkelling etc), there are very many independent operators along the beach who will rent you a chair, take you parasailing, jet skiing or whatever you would want to do along a beach. Most hotels do not stop you from walking into their public areas to shop, use a restroom (also available on the piers) or eat. Most will stop you from using their chairs or sitting at their pool if you look like you do not belong. There are all kinds of shops , food and services as you walk along the path between the hotels and the beach.
Aruba also has some of the best shopping in the Caribbean. There are hundreds of independent shops and three major malls all with walking distance of the pier.
Aruba is a safe and friendly island.
I agree we went to Aruba on the Millie for the day. We just got off the ship and asked a cab driver to take us to a hotel, where we could use the beach. He said all beaches are open to the public. I do not remember the name of the hotel. It was big and beautiful.
We walked through, rented chairs. We had a great day.
I enjoyed browsing the main commercial strip near the pier.
SInce I like exotic & imported foods, I made a point to detour to the supermarket district (a short bus ride from the bus depot). The large assortment of Dutch imports and local brands was worth the journey.
If you like to snorkel take a trip to Baby Beach at the southern tip of the island. The entire island is only 19 miles long -- so its not too far. Also, it is very easy to just rent a jeep right at the pier. IF you are feeling adventurous and you have the time, 4 wheel over to the far side of the island ( which is only 6 miles wide but the roads are virtually paths) and go to the natural pool and natural bridge. Just make sure you dont miss the boat!