We went to Naples a few years ago and got a fairly central hotel, old-fashioned but comfortable, through a booking agency, Venere, which DH has used a lot, and which has taken us to good hotels, not too expensive, whenever he has used it. We were there for several days and found the public transport easy to use and just followed the advice to keep all eyes peeled for pickpockets. One night we were going to bed when we thought we heard fireworks at some distance, but the fact that they lasted for only a short time and didn't sound quite like fireworks suggested that possibly it was gunfire. No obvious bodies lying around the next day though.
The only problem was crossing the road; we had naively believed that traffic in Italy drives on the right - not so. It drives, in Naples, on both sides at once and in all possible directions, including sideways. We were sure that we were going to end up in the middle of the road, stranded on a traffic island, hoping that people would frisbee pizzas to us. However, we survived, enjoying the pizzas at restaurant tables instead. DH wants to go back to go to Herculaneum (we just did Pompeii last time) and a museum which has a lot of stuff rescued from Pompeii. I wouldn't mind going back, but am a bit apprehensive about the fact that Vesuvius is well overdue to pop again 