Alitalia

First of all, full disclosure. I am an extreme worry wart about being on time for flights.

In my opinion, 3 hours is not enough time for what you want to do, especially if you have to retrieve any checked bags. Anything goes wrong, and you're toast.

A few years ago, we flew Alitalia from Catania to Rome to catch our homebound flight. We went up the day before, walked around Fiumicino, and had a nice dinner. No stress. You could do the same in Milan. Depending on your departure time (I assume not very early), you could sleep in the city, rather than at the airport. Milan has enough to keep you busy for a day, and it has lots of places to get good meals.
By the way, Alitalia was fine. Our flight was on time; our bags arrived with us.

If this connection is booked as a code-shared portion of your trans-Atlantic ticket, then your bags will be checked through to the USA and the airlines will be responsible to put you on the next available flight, in case of delay. Linate airport is relatively small, making transfers pretty easy, so I would be happy with 3 hour transfer time.

I have had unfortunate experiences with Alitalia in recent years, and would not trust them to get me to an airport on time. However, you'll find others who are fine with them – experience is very mixed.

If you are booked through on a single ticket and could survive missing a connection, then I think you're fine. If these are booked as separate tickets, or you absolutely have to make your connection, I would suggest returning to Milan the night before.

Are you sure your flight back to the US is from Milan Linate? I wasn't aware they had any nonstops to the US, so your flight is likely to be:

1. A flight from Linate to another European country to connect with a US-bound flight - see below.
2. A flight from Milan Malpensa nonstop back to the US. If this is so, your plan will not work, as it's quite a long way between Linate and Malpensa. You will have to get to Milan the night before.

If you are flying out of Linate, the question is how lucky do you feel? It's not a matter of whether Alitalia is reliable; a flight can be delayed or canceled for any number of reasons. What will you do in that situation?

In a similar situation (Sicily to Rome to the US), I flew to Rome the night before. I would have been a nervous wreck doing it any other way.

Like Harold, I'm surprised that your trans Atlantic flight is connecting in Linate.