For a relaxing and inexpensive tour of the city hop on one of the orange city buses and enjoy the scenery. The buses are only one euro to take and the ticket lasts for 60 minutes so you can make connections if needed. The bus goes all over town and most important to the main port and Marina Grande which are long steep walks. The tickets are sold in tabacco shops and some hotels. You may want to see if you can print out a route map before heading to Sorrento or see if you hotel or campground has one.
The one trip not to miss is the end of the Capo Sorrento line. Follow the signs to Roman ruins and after a 10 - 15 minute walk you arrive at a beautiful rock beach into the Sea of Naples. This is a fairly grueling walk so make sure you are in good shape and well hydrated. You will find some locals sunning themselves on the rocks and maybe swimming. Again this is not easy access to the water but it can be done if you are in good shape and have a sense of adventure.
With Sorrento as our home base, we took a day trip south to the Amalfi Coast. As my guidebook says, this is "one of the world's great bus rides. It will leave your mouth open and your film exposed." We made sure to sit on the right side of the bus to get the best views of the Mediterranean from the road on a cliff 5oo feet above the water. Those on the other side of the bus really missed out!
Our destination was the town of Amalfi. From there, we took a short and even curvier bus ride up to the town of Ravello where we found a spectacular ceramic plate.