Napoli is a lively city at night as well as during the day. As soon as the sun goes down, it becomes a very interesting universe of joyful people, kids playing football, girls wearing the best dresses just to impress, families, couples and singles, it is a place where everything is possible, even some bookshops turn into vibrant bars or the fishmonger shops into smart fish restaurants.
Bars and restaurants are open until late and are always busy. For late I mean, really late almost until dawn. Some could be scared just to go out in the 'dangerous' alleys of Napoli. It's nothing like that. I have been living in Napoli all my life and I have always felt safe. Just take the usual precautions that you would do in any other city. I actually found that many tourists get used to this night 'lifestyle' very easily. How could you not.
Especially in Summer, when the schools are finished, the heat is more gentle in the evening, from the promenade to the historical centre, everywhere is always very crowded with markets, musicians or just people that can't sleep or don't want to. Everywhere is an interesting place to visit. It just depends of what you are looking for. You can have a pizza or a burger, to sit in or take away. There are also lounge bars and wine bars (enoteche), or listen to live classical music in an old churche or a dj set in a pub.
The areas called baretti which means 'little bars' have a lot of lounge bars, clubs and bars where you can have a nice drink and chill out with friends. There are many around Napoli and they are not only for the young people, there is a huge choice for every age. The old town, from piazza Dante around piazza del Gesu' and Monteoliveto is an area very crowded especially with students, in fact not far from there is a university. Here there are lots of pizzerias, restaurants, kebab shops and bars where you can have a nice cocktail or a shot for €2. Not far from here is the Keste' which is more than a bar, it's an art gallery with live music sessions.
In the posh area of Riviera di Chiaia you will find small and trendy bars with dj set music like the Kiki bar or many more around via Chiaia, via San Pasquale or vico Belledonne. There is no need for me to tell you which one is the best, there are so many and they are always full of people. A nice walk along the promenade to Borgo Marinari around the Castel dell' Ovo is a very interesting spot for restaurants and bars near the sea.
Going up to the hill of Vomero you will pass to via Aniello Falcone, another area full of baretti like Il Baretto, One, Baik or Flame. The bonus of this area is the stunning view of the gulf, which is not included in the price!
Once you are at the Vomero, there is a good choice of bars and pubs, like Goodfellas, where every night there are live tribute bands performing. There is the famous Fonoteca with a huge range of classic cocktails and music. Some other bars have on certain days of the week cocktails at fixed prices from around €1 to €3.
All the areas have very trendy and popular bars so for me it is not easy to recommend one in particular. The beauty of going out is not only the venue itself but what's around, in fact the night life is more outside, in the streets, in the narrow alleys and in the squares. It is this vibe that makes this city so unique and charming.
If you want to stay out until late be aware that much of the transports will close quite early (check the section Travel info of my website for metro and funicular timetables) however, you can walk from one place to another (for instance from the old part to the promenade is more or less 30 minutes) but if you are getting to or from the Vomero taking a taxi will cost you around €15.
A typical Neapolitan night out is not to get drunk, but to enjoy some good food, a chat with friends and few drinks. If you want to live like the 'local' you should go first to a pizzeria or a pub and then in one of those bars until you are not too tired. There is no rush, remember, you are in Napoli, and here having a good time is more important than sleep!