For particulars on where to say there are lots of threads in the forum. I just want to chime in on the points piece - Italy's just not a great place to use SPG/Marriott/Hilton points. Most of the properties are out of the way, but even those that aren't are usually at a points cost representing a poor value. Everyone treats points a little different, but just keep in mind that acquiring them isn't free, as much as hotels and airlines want to make you feel like you're getting something for nothing when using them.

If you don't need hotel services, I would suggest apartment rentals. Use a local agency if you can, but you'll find that a lot of them cross-list on Airbnb as well. Itaco is a good company in Florence and the surrounding area - they are locally owned and operated, pay their taxes, and do a nice job. They are bookable on Airbnb as well as their own website. I don't know them, other than being a guest in the past, for any avoidance of doubt in mentioning them. I don't have specific agencies for Rome and Venice as we're there less frequently and I'll just try and find things one-off, but others may have some apartments they'd recommend.