Relative to the Sheraton MXP, one tip if you have SPG status/app. If you have an early AM flight back to the States, leave but don't check out of your room. Wait till you are past security and then do it electronically (or just let the time lapse and they'll check you out).

The reason is if there is a flight problem or delay, you can go back to your room and relax a while.

One example: My wife and I were on a flight back to NYC via MIA as the non-stop to NY was full in business. When we went to check-in the NY flight was delayed so AA wanted to re-route a lot of people on the MIA flight to catch (new) connections. They asked us if we were willing to switch off the MIA-LGA cxn we had for the now later direct to JFK. That would get us back to NY earlier and with a lot less hassle. We said sure, checked our bags and then went back to our room at the Sheraton to relax for 3 hours before we had to walk back to go through security. While we had lounge access, the room was much more comfortable than sitting in a lounge for all that time (we did spend 30 minutes in the lounge anyhow).