Ponza is an island destination mostly frequented by Italians (especially Romans and Neapolitans, as it's just a hop, skip, and a jump away by boat) that is largely undiscovered by foreign tourists.
One of my favorite beaches accessible by foot (there are many beautiful beaches and inlets in Ponza that are only accessible by boat, due to the dangerous rock collapses from the above cliffs that have happened previously) is the Piscine Naturali. To get there, take the bus from the port to Le Forna chiesa (there's only one main road on the island, so all buses go there - you just have to ask the driver to tell you when to get there). From the church (chiesa), follow the signs or ask someone to direct you to the Piscine Naturali. It's a long walk down (and an even longer walk back up at the end of the day) but it's worth it. These natural swimming pools formed in the rock are the perfect comfortable place to sunbathe and easily get in and out of the water - which should not be taken for granted in rocky, cliff-filled Ponza! There are some makeshift coffee bars built into or on top of the rocks where you can buy sandwiches, soda, water, ice cream, etc, so you don't have to worry about packing a lunch. Rent a lounger to sunbathe comfortably or spread your towel out on a rock. Dip into the warm water of the natural swimming pools - and bring your snorkeling mask, because you will see fish, sea urchins, corals, and more.