The most beautiful place I've ever been is this lovely island named Ischia. It's just west off the coast of Naples, and just north of the better known island of Capri. This was the location chosen for our first weekend getaway in Italy, and boy did we make a good decision! The island was not full of tourists as most places in Italy are, but rather we found beautiful tropical flowers, picturesque beaches, and the best local wine and cheese. Not to mention, the pizza in the entire Naples area is to die for.
Naples is known for being a rather dangerous city, however when our group was there, I didn't necessarily feel threatened or unsafe at any point. I think as long as you are aware of your surroundings, your bags, and your actions, then you will be fine.
One of the "must-see's" at Ischia is without a doubt the Castello Arogonese, a castle built in 474 B.C. which you can tour for only 10 euros. The views and history of the castle are unrivaled, as well are the peaceful walks one will find wandering through the old churches, olive gardens, and look-out points.
If you do plan on visiting, here's a helpful tip. You can get to the island from the Naples port one of two easy ways. First, you can take a hydrofoil for roughly 18 euro which will get you there in a matter of maybe one hour or so. The other is to take a ferry. While significantly slower, is also significantly cheaper at 5 to 10 euros.