Re Naples itself, we had many, many fine suggestions from Acraven in response to the following query: https://community.ricksteves.com/travel-forum/italy/naples-and-environs-suggestions-per-favore.
As to our trip, we had 3 days. 4 nights in Naples.
Our highlights were the archaeology museum, a private guided tour of Pompeii, Spaccanapoli and its street life as well as churches in that centro historico neighborhood including the Duomo, the Tesoro, as well as Gesu Nuovo. (Due to bad timing on our part, we missed Miseriocordia and Sansevero.)
There are two RS Audio Europe audio guides worth downloading. One is for Naples’ Archaeological Museum and the other is the Naples City Walk.
Our other great highlight was a lovely day trip to Ischia, though you may not have time for that.
(Our one disappointment was Museo Capodimonte.)
For more about our experience, perhaps our TR will be useful. SEE https://community.ricksteves.com/travel-forum/trip-reports/southern-italy-30-days-three-ways-to-travel.
To answer your Q re getting to Pompeii, there is a train from the main train station (accessible from the Metro) that goes to Pompeii (and further on to Sorrento). That’s about a one hour train ride, once you get to the Naples Centrale train station and then on board.
For better or worse, we stayed at the Hotel Decumani de Charme. Well located if you’re ok being in the gritty part of Naples and it’s an easy walking distance to the centro historico. The hotel was shades of past glory. Breakfast is in a fabulous dining room, but I would give the meal itself a sorta ok rating. The hotel is located on a quiet street. :-). The rooms were nice and clean and staff was good.