Capri is a small island so, in the height of summer, it can be unbearably busy so when opportunities for 'getting away from it all' present themselves, you must grab them with both hands. One of the easiest ways is to hire a boat and find your own little spot for dropping anchor and having lunch and a swim in a quiet cove, or take the chair lift up Monte Solaro and walk down.
How I’ve picked my things to do:
You're unlikely to be on the island of Capri if you want to get away from it all (in spite of my advice above). You're more likely to want to see and be seen and so I've included a few more touristy attractions along with ways of experiencing the beauty of the island.