3 days in Naples

Pastries!

Other than that, the Archeological Museum, cathedral, and Cappella Sanservo are all close together in the center of town. See them along with a stroll through Spaccanapoli for the quintessential taste of Naples. If you’re an art person, Museo Capodiamonte has some terrific paintings, though getting there and back can be slightly tricky. Since you’re staying in Naples, I’d advise you to seek out some of the highly rated pizzerias that are just outside the city center. (No longer have the links, sorry.)

Herculaneum is also very close to Naples, and takes only a few hours to see. Not quite as intense a day trip as Pompeii, but equally fascinating. It is often open quite late as well. You can totally see both sites in a single day as long as you manage your time.

A few ideas: 1. Hotel There was a mix up with our hotel and it was 10:30pm! Nearby, some college language students were sitting at a table and I asked if they could help my daughter and I find a place to stay for the night! We started walking down the street while they called friends and places they knew. We stopped at several places that were all booked, but this place wasn't: (Sorry for the Booking.com website, but I wanted to make sure it was the right place! We were only able to stay one night, but I wish we could have stayed longer! Breakfast was amazing!) https://www.booking.com/hotel/it/b-amp-b-bellini-napoli.html?aid=311088;label=b-amp-b-bellini-napoli-vtqm9B0pPD6N5_3jvOnRLQS169133497627%3Apl%3Ata%3Ap1%3Ap2%3Aac%3Aap1t2%3Aneg%3Afi%3Atikwd-14161891515%3Alp9033276%3Ali%3Adec%3Adm;sid=bca95b5e6321438020ac3bf093e051c0;dest_id=-122902;dest_type=city;dist=0;hapos=1;hpos=1;room1=A%2CA;sb_price_type=total;srepoch=1532315196;srfid=dd9167b3b0057c0a485f67f27500057ee5a6c1adX1;srpvid=092115dd43eb0114;type=total;ucfs=1&#hotelTmpl
2. Stay in different places nearby and make a loop. Start in Naples, Vesuvius had wildfires on it last summer so we couldn't visit. Instead we went to Herculaneum and Pompeii in one day on the train and back to Naples. Very long and tiring day! If I did it again, I might continue south to Sorento or vicinity for the night. Take a boat to Capri and or Ischia and spend the night then go back to Naples.

3. Food: Try the little kiosks with little cups of fruit. The melon was the best like a fruit juice slurpee with little chunks of very ripe and delicious melon! Find a top rated Napoli pizza place and get it to go since you won't have to pay the cover charge! We were on a budget!! In Naples we found a yacht club and were able to walk next to the marina out onto the rocks and see Mt. Vesuvius smoking from the fires and fun to see the view from the rock wall and fishermen. Some were swimming, but we didn't have our swim suits. Have fun!

You have more than enough time to get a guide book a read it to find what out what you are interested in and can't miss
Or when you get there ask the local concierge. I was there last May and nothing stands out as something not to miss.

I agree you might find more going on long day trips from there to for example Pompeii or Paestrum.
But again it depends on your interests and you need a guide book ebook something like that

Thanks everyone for all the tips. Already had Pompeii and Capri on my list. Glad to find out about Herculaneum and those little fruit cups!

I just posted this elsewhere and thought I would share it more generally.
Regardless of your religious beliefs, you might enjoy seeing shops in Naples that are world famous for creating and selling what in my family are called "nativity scenes" and sometimes called "creches" "manger scenes" or in Italian "presepe" : statues that recreate the story of Jesus being born in a stable including statues of Mary, Joseph, the baby Jesus in a cradle, along with barn animals as companions. Apparently in Naples, this is taken to a high art form and all sorts of characters are carved so that they too can be part of the scene...statues of bakers, fishermen, house painters, bus drivers, nurses, and just about anyone else you can think of (including celebrities). The stores are on the following street: "via San Gregorio Armeno. It is located in the centro storico, or historic district of Napoli, this street has hundreds of shops featuring hand-made presepi." I have not yet seen it but I plan to do so during our upcoming trip. I'm sure some of it is tacky, some impressive, but it is something Naples has been known for hundreds of years and I would think your daughter will remember it for many years!

More info:
https://www.lagazzettaitaliana.com/history-culture/7741-the-presepe-tradition-of-naples-italy
https://www.tripadvisor.com/ShowUserReviews-g187785-d195422-r418055023-Via_San_Gregorio_Armeno-Naples_Province_of_Naples_Campania.html