This place is nothing short of amazing. It is even bigger than it seems on the pictures, every room is very spacey and lovely furnished, it feels like being in one of these old italian movies. Every room has access to the large terrace that surrounds the whole apartment - which even has a sea view and is surrounded by lemon trees. The kitchen is fully equipped and pretty big, including a gas-oven, so you can cook amazing italian food there.
The area of Posillipo is very lovely and a little quieter than the city center, it is perfect to stay there and explore the lifely city of Naples. You have everything you need in walking distance though: shops, restaurants, cafés and a public space where you can get an espresso and oversee the Vesuvio. Everything is very authentic and the people are super nice here. The Bus 140 takes you to the city within 30 Minutes, though the walk down has some amazing views so it's also worth it.