If I may suggest something.... Over the years we've known this area, the local Time Out guide has consistently been the best - its current edition can be had for about £9....
http://www.amazon.co.uk/Time-Out-Naples-5th-Guides/dp/1846701023/ref=dp_ob_title_bk
... money you won't regret spending!
,,,,,,,,,,,,,,,,,,,,,,,,,,
If you're 75, your Mum will almost certainly be happier in Sorrento - but hopefully that's part of a DOB ?
In October, give or take a few spectacular thunderstorms, the weather should still be very pleasant - here's how nearby Ischia looks that month...
http://www.pbase.com/isolaverde/recoct
.... so you might split your visit - for some city time, and a few days by the sea... possibly taking advantage of weekend offers in the city, and weekday ones at the coast?
Try this little Campania-wide guide, produced originally by the regional authorities...
http://www.bb-napoli.com/english/seaguide.pdf
... or one that covers just the province of Naples:
http://www.com-tur.com/documenti/manifestazioni/003/perledelgolfo.pdf
,,,,,,,,,,,,,,,,,,,,,,,,,,
Naples hotels can be rather hard to fathom, particularly given the way prices move over the year! Even if it's slower, check prices on the websites of those in any area you like - rather than relying on 'averaged' costs, or how many stars they've got!
I've not looked at costs, but a couple of places which friends and family have used after visiting us here...
This one's just off a popular shopping street, handy for many of the sites and sights:
http://www.tripadvisor.co.uk/Hotel_Review-g187785-d267249-Reviews-Chiaja_Hotel_de_Charme-Naples_Province_of_Naples_Campania.html
http://www.hotelchiaia.it/en/
... or, a bit dearer but insisted on by our friend 3 times...
http://www.tripadvisor.co.uk/Hotel_Review-g187785-d202910-Reviews-Renaissance_Naples_Hotel_Mediterraneo-Naples_Province_of_Naples_Campania.html
http://www.marriott.co.uk/hotels/travel/napbr-renaissance-naples-hotel-mediterraneo/?pid=corptbta&scid=b661a3c4-9c47-48c8-9e13-75b66089dd79
Although we rarely stay in the city - preferring to come home at the end of the day - I'd suggest looking in the Chiaia and Mergellina area, a favourite of ours and nicely near the sea with some lovely walks and views:
http://www.pbase.com/isolaverde/mergellina
But best, I'm afraid to say, to avoid Piazza Garibaldi for a while yet - despite some decent hotels often offering great bargains....
As these from last month show, still a way to go before the construction work there is finished:
http://www.pbase.com/isolaverde/image/143257843
http://www.pbase.com/isolaverde/image/143257844
Peter