We are staying in Sorrento and have a 6:15 am flight out of Naples. So I guess we will have to get a hotel for that one night. Any suggestions of where a family of 4 can stay that is safe and has easy access to the airport and what time should we plan to arrive at the airport?
Hotel piazza Bellini is not a bad choice. It is about a 20 mi ute cab ride to the airport, and it's a nice hotel.
Oh, and the cab ride should be about 16 euros.
Ask the hotel to reserve a taxi for you - you'll probably pay the higher night rate. How early you need to be at the airport depends on your destination after Naples (if you are connecting in another European city it's considered a domestic flight).