Apartments in Sicily

Have you looked at AirBnB - I looked under whole house/apt and there are at least a dozen listed in Palermo.
Let us know what you find - Apt. sounds great for Palermo.

Booking.com also lists apartments. Other sources are VRBO, Homeaway...

Here's my review of the small house (2 bedrooms) I stayed at in Ortigia. I'd definitely stay there again: https://community.ricksteves.com/travel-forum/italy-reviews/siracusa-airbnb-in-ortigia

I just booked one on booking.com. I haven't stayed there yet, so can't recommend, but there were plenty listed on that site in your price range. Take a look there!

Thanks Harold for your apartment suggestion. I will check it out. Thanks everyone else for your responses regarding sites that rent apartments. I am aware of and have checked many of them. There are so many options, often with no or few reviews, that I am looking for replies about specific apartments that people can recommend in those cities. I'd love to see a few more of those if anyone out there can help.

I'd be leery of booking any place that doesn't have a good number of online reviews. The older buildings in Sicily may have archaic plumbing systems. You'd probably like to know in advance whether you will, or will not, be able to flush toilet paper. There's a second unattractive possibility that you might encounter in an old building: a noisy grinding mechanism that kicks in not only when you use the toilet, but also when you run water in the lavatory for more than a few seconds.

Good to know, acraven. We have booked two apartments in small towns. Still checking out options in the larger cities.