Hi Arnold, nice to meet you.
The location you chose is very suitable to visit a lot of interesting places. Naples historical center is a short step from you and has a Greek map, formed by three Decumani (parallel streets) and many Cardini (ortogonal roads). You just have to walk throug this network to wonder in every corner. :-)
These three Decumani are: Lower Decumano, as known as "Spaccanapoli" (Via Benedetto Croce and after Via San Biagio dei Librai), starting from Piazza del Gesù Nuovo; Medium Decumano (Via dei Tribunali) and Upper Decumano (Via dell'Anticaglia/ Via Donnaregina).
Firts of all you MUST visit the curch and the cloister of Santa Chiara (http://www.monasterodisantachiara.com/), in Via Bedenetto Croce: its majolica courtyard is a rare example in the world. Just in front, you will find Gesù Nuovo Cathedral (http://it.wikipedia.org/wiki/Chiesa_del_Ges%C3%B9_Nuovo); the main facade of the church is famous for the wall in "bugnato", arourd which there is also a misterious history ;-)
Another MUST is San Gregorio Armeno, typical for "presepi". Please visit the church of Santa Patrizia (http://it.wikipedia.org/wiki/Chiesa_di_San_Gregorio_Armeno) and ask nuns you will find there to visit the courtyard: it is not well known, but, believe me, you'll find it wonderful! Please offer few euros before leaving: nuns use them for poor children.
Then, you can't leave Naples without visiting the "Cristo Velato" in Cappella San Severo (http://www.museosansevero.it/it/). I don't tell you anythig: go there and you will be surprised!!!
If you want to visit a wonderful church, follow the Upper decumano till the end, in via Carbonara and you ill see the cathedral of San Giovanni a Carbonara (not on Sunday).
When you will walk along these street, please look inside the portals: you will see wonderful yards and majestic stairs.
Pay attention to every step you take, because this is a magical place and every corner hides a wonder: a building, an old and maybe forseken church or chapel, a little workshop, or something deliciuos to eat.
For other locations outside Naples, you need to pledge a day for each one. In Piazza del Gesu there is an info point where you will find roadmaps and timetables.
These are only few of the many many things you could see in Naples. I hope you will come back for a longer period. For the time beeing, enjoy this charming place and have a nice stay.
Carmen
