Our hosts were wonderful, the apartment is sited perfectly, 3 blocks from the Centrale train station and right around the corner from the gates of the old city, markets and special places.
The apt itself has been in the family for generations, on the 2nd floor with a wonderful old antique lift bringing you up, furnished with period pieces in the sitting and bed rooms with the bathroom and kitchen having been brought up to date with modern appliances.
We took the circumvesuvio train to Herculaneum (our fav), but you can take it to Pompeii and Sorrento as well.
The #1 metro (at the train station) stops at many of the places you want to visit and their is a guidebook devoted to it (provided). We purchased day tickets at the station (lower level) and made good use of them.
We were extremely pleased with the period character of the apt and enjoyed the inexpensive local food and restaurants. A quick Pizza down the street to warm and enjoy was 1.50 E
Napoli is dirty and earthy but is a vital, don't miss experience. We'll be back.
Last tip: Half way back to the train station: La Cantina dei Mille...a few tourists, but mostly locals...eat inside...skip the expensive specials menu...
We ate there twice, loved it...the 2nd time you will be greeted as family...(maybe not the first). One (large) shared pasta, 2 or 3 mains, wine and water for 32E...Food great, mussels, not to be believed. All seafood fresh and simply and tastefully prepared...On a whim, I ordered roast chicken and loved it.