Here s where I d start,,first get a good guidebook
and also google tourism in Naples...If you don t want to rent a car,,,get a good guide(check out references,etc).use internet sites to find hotel(or use your points).
We had a car for out of town trips,,but its a hassle in city,crowded and no parking.
We took boat to Capri for one day,drove to Pompei,,saw Vatican when in Rome(its a long ride for 1 day tour).
Lovely city,, I tried to speak Italian,,and most answered back in broken English(and we used a lot of hand signals,,haha).Naples can get a bad rap,,,but we loved its "gritty,lived in"feel.