I've stayed in Naples in the beginning of march for 3 days.
The trip from Naples Airport to the city can very easily be done by ALIbus.
I've stayed in the UNA hotel at Piazza Garibaldi, for me a perfect location opposite of the central station. I arrived pretty late so I only enjoyed the lovely view from my room.
On day 2 I took the R2 busline to Via Chiaia, very beautifull spot in Naples. I find the system of buying public transporttickets at the Tabacchi very easy, only € 1.10 for 90 minutes! The busses are crowded all the time but run frequent, a very good option to explore the city. I've found the area near Galerias Umberto very beautifull, nice shops and great small bars for the enjoyment of a cup of espresso. I was a bit shocked by the low pricing of many items in the stores, especially clothing in the many tailorshops are priced very reasonable despite being origin. For sending postcards I recommend the Postoffice in Galeria Umberto, very helpfull staff, as I found many Napolitans very helpfull!
As lunch I enjoyed a lovely lovely BaBa, wow, this is good pastrie! I bought the Baba at Grandcafe Gabinus, a very nice spot to enjoy a drink and some pastry, lovely terrrace!
In the afternoon I went to visit Capri, trip to Capri is very convenient by Boat, tickets were a bit expensive, paying 32 euros for a round trip! Capri itself is beautifull, perhaps a bit touristy but worth the trip!
I've enjoyed dinner at restaurant Rosati, in my opinion a good place, besides being to only single next to couples I felt welcomed by the staff and enjoyed a typical napolitan pasta.
Despite of some other reviewers I found Naples pretty safe and comfortable, ok the place near Garibaldi is filled with salesman and prostitutes at night you can easily walk there in the evening, just don't interact with people you don't want to interact with!
On day 3 I had to make a short businesstrip to Vallo della Lucania, I went to the Central Station and found the ticketmachines very easy to handle. The train hat a delay which gave me a change to walk around a bit, many guys try to sell you different stuff, most of it fake Louis Vuitton, Gucci etc but all very polite. I've your looking for a bargain this is your place.! Altough I wouldn't recommend you to buy cigarettes on the street as they are obviously fake.
The trip to Lucania by train was beautifull, via Pompei and the coastline, really spectacular views along the route. After returning to Naples I decided to go out for dinner at Pizzeria Starita, wow what a great restaurant! Best pizza I've ever had! Starita can easily be reached by metro, stop Musea.
On day 4 I decided to check out the area around Piazza Bellini, also a very beautifull area with nice shops and some very good pastrieshops! In the afternoon I took the Hop On bus from Piazza Municipale, I must say I found the ticket pretty expensive compared to other Hop On busses across Europe, I believe I've paid about 24 euro's. I must confess that the ticket is valid for 3 different lines, 2 for the center and 1 for a trip towards Via Manzoni where you can enjoy breathtaking views from Naples and the coast! With this last tour my trip came to an end.
Overall: I loved Naples, liked the people, to me they were all friendly and polite even after my famous line: " Scusi, non parlare Italiano, can you tell me how to get here"? Most of them pointed me the location on my map and helped me out! Cuisine is perfect in my opinion, pure and very tastfull! The city offers enough special sites and I just worth walking around until your feet give up! Naples thank you! Grazie!