The apartment is nicely renovated and in a very convenient location.
I would definitely take into consideration the recommendations made by Fabrizia.
Also, if you are looking for a drink or lunch I recommend near the music Conservatorium, so you can benefit from the music coming from the school.
There are a LOT of stairs to get to the roof top apartment, it has a lovely view, but if you have bad knees I would recommend you take this into consideration.
There are lots of sites to see locally and it was very easy to catch public transport for Pompeii.
If you want to have a meal or shop in a more up market area you will need to head to the Port.