Personally, I would head to Reflexions Beach Bar and Restaurant right near the cruise port. Beautiful beach, loungers, shade, food, and shower/bathroom facilities. Palm Beach does have shade and chairs available to rent at Moomba's. Eagle Beach has places to rent across from Amsterdam Manor, MVC, and a little further down the beach. Baby Beach is a long cab ride. If your heart is set on it, I would rent a car for the day. There is a restaurant there, a bathroom you need to pay to use. You can rent shade and loungers, as well as snorkel gear. There is also a restaurant there.
Is there a fee at that one? I like that’s it’s only a mile away...
Baby beach is probably too far away. It's about a 25 drive to get there. Another option right across the port is in the renaissance hotel. You have to pay $125 pp but you'll get to go to their private island with great beaches, snorkeling and don't forget the flamingos. The restaurant on the island has the best pizza I've eaten in Aruba. Try the Hawaiian.
If not eagle beach is about 10 minutes away.
Renaissance private island is first come, first served. You arrive early and they only allow it if the hotel isn't at full capacity.