I'm not current on Amex FHR in Rome, but Perche's comments are very accurate. I haven't stayed there but I agree the Inn at the Roman Forum looks particularly interesting. JK Place is also well regarded - the location depends on what you want to do, but we liked walking to Villa Borghese from that part of the city. The Vatican is also walkable. Most other things you may want a taxi if you don't want to do a lot of walking. 5 stars in Italy really doesn't mean much, though, more of a checklist of what a hotel offers versus any regard to the quality of that offering.

On the St. Regis Rome, I've stayed there and I have no particular desire to return. Cavalieri is in a bad location for me.

As for Florence, my go-to upscale hotel there is Hotel Lungarno. I'd avoid the Four Seasons (too far out). The Westin Excelsior and St. Regis are well located, but they don't feel as Italian to me. My favorite place, though, is an apartment in Granduomo - this place is limited service, so if you're expecting a lot beyond a room, housekeeping, and a very Italian breakfast (bread) at your door, it's not for you. But the deluxe apartments facing the Duomo are nice, especially one with a balcony. Itaco is also a good company with some short term apartment rentals - they list on Airbnb if you're more comfortable with that.

I was an Amex Platinum cardholder for years, and the only FHR hotel I ever stayed at in Italy is Hotel Lungarno. It's a great place, but spring for something with a balcony/terrace on the river side. Based on what you're saying you'd prefer, I think that's your best bet.