Jenny, I would be very cautious especially exiting the railway stations which are absolute thieves kitchens. Last time I changed trains there, they were revamping the old central station which was still taking trains full of unwary people into a rather abandoned demolition site, with the 'proper' new station a good brisk walk through down the road through a poor and quite dodgy neighbourhood.
At the central station pickpockets hang especially around the ticket machines - I had a guy try to dive between me and my credit card (he didn't win).
Naples has always been a bit lairy but in the last decade the influx of migrants from the north African route has contributed to street problems in many of the Italian towns, especially those on a train route to Rome.
It's a shame as the museum is meant to be brilliant, but if you are going to visit I suggest you do so in a group or with a tour.
Sorry to sound negative but safety first.