We stayed at the Hotel Palazzo Decumani Via del Grande Archivio , 8 Napoli 80100. They have some very big, very pretty rooms, although the views are of gritty Naples! In October I hope their excellent, savage air conditioning (!) will not be as useful for you as it was for us. This was 2014. I think the same group has some other hotels. Perhaps the key information when I was researching was that it was a complete, gut-renovation of an old palazzo.
You will find it hard to believe, but we walked to the Archaeology Museum and later to the main Train Station from here, but they were both VERY long, scenic walks.
EDIT: I meant, just above, to indicate how FAR it was to the train station, not how close!! But we had only 24 hours in Naples and were happy to see as much of it as we could.