You state that location is important, then you should be happy that the Hilton is way too pricey, its very far out of town. Beautiful views but not convenient to anything.
As for renting apts, I've done this on a # of occasions. It may or may not turn out to be cheaper. A couple of other things to consider: many rentals run on a weekly basis, so finding something for three nights - esp. in high season - could be a problem. Also, be sure to confirm the availability, use, and price of air conditioning up front. I know more than one visitor who has booked a place w/a-c only to be told they have to pay extra for its use, etc..
Don't let the name confuse you, but I've used the agency
http://www.venice-rentals.com
on more than one occasion for Rome, very good apts, very trustworthy agency. You might also look into hotels that have family rooms. IIRC the Hotel Cesari in Rome has family rooms. Great hotel located just behind the Pantheon.
Finally,
ChgoBob provides excellent advice re: Naples - Keep your wallet/valuables close, including your luggage on the train.