Hi,
The Nearest beach is Cala Mayor, Very near the port 10 mins in a taxi you could walk in about 30 mins.
https://www.seemallorca.com/beaches/cala-mayor-beach-palma-de-mallorca-cala-major-(beach-resort)-664263,
Not my choice if you want a quiet beach, this is a very small beach ,lovely setting ,20 mins by taxi ,going back to the port you might have 10 min walk into the village of Portals nous where there is a taxi rank or the bus .
https://www.fincallorca.com/mallorca/beach/cala-bendinat
You will find it a struggle to get back it is at least 4.5 hours , I would not take a chance on the catamaran tour.
Roger b