Reading through the suggestions and your interests I have a modest proposal - move your Naples days to Salerno instead.
ChristineH is correct Naples is a lot. I don't know your history of large, chaotic cities but Naples can be a lot even for the seasoned Italian tourist. Salerno gives you excellent access to Paestum, pretty good access to Pompeii, and easy access to Naples via the train for the Archeological Museum and other Naples sight seeing. It also gives you a small taste of the southern chaos but in much more manageable doses than the full-on Naples. Capri is pretty far from Salerno but there are ferries to the Amalfi Coast from there.
Just a suggestion - if you are willing to tackle Naples head on good for you! But you're also doing mostly big city Italy so I think a little time off may give you some relaxation from big, busy city Italy since most of Italy is actually rural and small towns.
Also I always advocate being in the city you're flying out of. I have not always done it myself but I try to. As always in Italy - especially in the south - have a back-up plan. The problem is Naples is 2.5 hours away from Rome even by car so if you have train problem and decide to switch to a bus you're 3+ hours away when you start and there is no easy answer to make faster.
My $.02, always it's your trip and this is all just advice,
=Tod