There are many small day trips you can take from Sorrento or Positano (Amalfi, Atrani, Praiano, Ravello, etc.) via ferry boat. We recommend visiting the island of Capri! Take a cable car to the top of the island (or brave the long, uphill walk) and enjoy beautiful restaurants, shops, and scenery! They also have pristine beaches and boat tours to the famous Blue Grotto.
We are not going to recommend specific restaurants, because you CANNOT go wrong. Out of all of the times we have been to Italy, we have yet to have a meal that did not exceed our expectations. You are going to one of the food capitals of the world, so foodies - enjoy!
There are a few spots that are considered free public beaches, but the majority of the shoreline is owned by various beach clubs. This is great because you have access to restrooms, food, drinks, deck chairs and umbrellas. But be prepared to pay! NOTE: don't plan to be barefoot unless you have tough feet. The beaches are made of pebbles!