We then walked down to the other side of the island to relax at Da Luigi ai Fariglioni for swimming in the Mediterranean and enjoying the craggy views. Beware that there is a charge for sunbeds and umbrellas, as well as towels. Also, if you wish to dine at the restaurant, there is a cover charge. Food was great, but many bees.
Finally, the shuttle to Marina Piccolo (NOT the cruise marina) doesn't leave until 3:30. If you have a short day, talk to the lifeguard and he can book you a private water taxi for about 20 EU per person, which can be a beautiful way back to the port.
The kayaking was great to give a different perspective - because since we climbed the walls in the late afternoon, we could really get a good feel for where we were.
BTW, do NOT climb the walls before 4. It is way too crowded and hot! Wait until late afternoon, and you will thank me later!
The best part about this beach is that there were absolutely only locals. Clear, beautiful water, but a very pebbly beach so bring water shoes. Also bring snacks and drinks because there ain't much around them parts.