You are going to get the best advice about Florence from PWMTrav, and not from me. I can help a bit when it comes to Venice and Rome. I'm not a pro when it comes to using Amex FHC, but here are my first thoughts.

Forget about the star system. It doesn't exist in Italy. It has nothing to do with the quality of the place. There's some legal mumbo-jumbo when it comes to stars there, and it varies by region. A one star hotel can be better than a 5 star. It really makes no sense at all. For example, to get to 5 stars, you must have 24 hour reception. I can't think of any place in Amalfi that has 24 hour reception, unless you want to knock on the door hard enough to wake somebody up. And also, to get to 5 stars you must have an elevator. There are hotels in Venice with an elevator, but the first elevator went in when an elderly gentleman on Fondamente Nova just could not put his wife in a nursing home and she just couldn't do the stairs anymore. So he had the first elevator built. I don't remember the year, but it wasn't too many years ago (I guess, depending on your age perspective.).

You can't be a 5 star hotel if you don't have an elevator. Since most of the hotels on the Amalfi Coast are only one or two stories, they don't need an elevator, and never get to be 5 star.

The rules vary by region, but another one is that to be 5 star the hotel has to offer breakfast. It's just a fact of life that Italians don't eat breakfast. In a country where the restaurants don't even open until 8 at night, nobody is so hungry in the morning that they need pancakes, waffles, and and egg omelet (by the way, in Italy, eggs are eaten for diner; not for breakfast). So a 5 star hotel won't even be held to Italian authenticity standards because of the breakfast rule.

I'm quite sure the star system also depends on the size of the lobby. So you can be in a five star hotel with a huge lobby and eat pancakes and eggs, or be across the street in 3 star hotel where you would have a smaller lobby, walk outside and have better coffee, and eat the only thing Italians every have for breakfast: pastry.

In general, things in Italy are small, so to meet the requirements of 5 stars in Rome, few hotels in the city historic center will be able to do it. And the worst mistake you could make would be to stay in an American style chain hotel that will be outside of the city center. That's dreadful. I suggest that you drop the idea of stars, because there is no Italian equivalent. I think that in Rome the only requirement to be a 5 star hotel is a large lobby, to have a bell hop, to have 24 hour reception, and that the room gets cleaned once a day. Although it varies from region to region, the star system is not very reliable in Rome.

Of the places you mentioned, Cavalieri is way too far away to be useful. I cannot imagine a worse place to stay, because of location. On a business meeting where you are not there to enjoy the city, OK. Someone put me up there (on a business meeting) and I couldn't wake up fast enough to check out and get to Rome's downtown historic center. Russie is supposed to be fabulous, the location is OK, but I've not been invited to stay there and it's out of my budget. Not really, but who wants to stay in a hotel in Rome where they serve breakfast? I don't believe the value for the money is there.

Now, the Inn at the Roman Forum sounds really interesting. 90% of a hotel's interest is based on location, and different people can scale that up or down. Staying near the Forum or Colosseum is generally a loser. Too many people harassing you to buy things. That hotel is just across from a divide that makes it somewhat inaccessible to most. I had an apartment around the corner for from it for about 6 months. I still have a gym membership around the corner on Via Baccina. When I go Rome that neighborhood is exactly where I look for a place to stay. I'd say that it isn't going to be everyone's choice because it is not tourism driven. It's a regular neighborhood. But it wouldn't take you five minutes to walk to the Forum, maybe 15 minutes to the Colosseum, and you would be away from the crowds.

I have no idea about the interior of the hotel, but I have lived around the corner. I can just say that I would rather stay there and pay, than stay at the Waldorf Cavalieri for free. It's an absolutely spectacular neighborhood.

The Saint Regis is two blocks from the train station. I would only go there if someone put a pistol to my head. You will not be experiencing anything about what Rome has to offer by staying there.