I usually choose places first and hotels second and if the two combine, well, that's a miracle. Places like Paris are destinations and, let's face it, no matter what hotel you are staying in you are not going to be in your room very much. And I'd much rather stay in a more characterful Paris hotel than the FS and spend more money on a nice dinner. The same applies to Rome, Florence, London, wherever.
Which brings me to the Villa F. I have never stayed there. I quite like the look of the place but it's not in an area where I would enjoy. However, I can see quite easily that it's like a resort, on its own, with the lake, you don't need to leave it, you are treating it as a a destination. So that's where I would go.
Amalfi? That was lost decades ago.