When we arrived, we were hustled into a flat-fee ride for 25E to the airport. The hotel told us it should have been 10-15E. Not sure if you can have the hotel arrange anything, but whatever you do, just be aware of your surroundings and possessions.
We didn't make it to Capri. Depending on your time, Sorrento is an easy trip from Naples...same train goes from Pompeii to Sorrento and you can ferry back.
My wife is a history buff, but you can easily do a walking tour of Pompeii if you get there when it opens, take the train to Sorrento for lunch and dinner and ferry back to Naples. The Naples Archaeological has a lot of Pompeii artifacts. Check the schedules. When we were done in Pompeii, we thought we'd go back to Naples for the museum but realized it was closed that day.