We will be in Milan for 2 days the first week of July. We would like to see as much as we can and would love to get opinions on best places to eat lunches and dinners. Recommendations for must-see sightseeing would really be appreciated. If you can break it down into Day #1 and Day #2, we would be so grateful. We are arriving in Milan and then taking the train to the Hotel Visconte in Milan. Thank you. Rachelle
Your request is too broad. It would be helpful if you purchase a copy of RS Italy book, or the Lonely Planet Italy book, and do your initial research based upon your own desires, rather than those of this Forum. If you do the initial planning, there are many on this Forum who can assist you in prioritizing the sights. Also, you say two days, and your time in the city is better calculated based upon the number of nights you are staying there.
If I only had 2 days, I would take a 1/2 day or whole day bus tour (which included several stops) The include the cathedral, the domed mall across the piazza from the church, the opera house and the museum at the opera and visit to the Last Supper. It was the best way for us to see most of what we wanted in a short time. The second day we took the city bus to the Cimitero Monumentale - easy local bus from next to the cathedral.
The Cemetery is amazing and we spent a few hours there.
AND of course walking around the area around the cathedral - nice restaurants, shops, museums etc.
The key sights are the Duomo and The Last Supper. The Last Supper sells out very rapidly, so if you want to see it, check on the ticket situation immediately. Many people end up having to take a tour that includes The Last Supper.
Bergamo is only about an hour from Milan by train and has a very atmospheric medieval district up on a hill. I'd try to get there if I had two full days in Milan.
When you go to the Duomo, be sure to go up onto the roof. Book your Last Super tickets as far in advance as you can.
Depending on what you're interested in, other sights include Sforza Castle (I especially love the Museum of Musical Instruments inside), Pinacoteca di Brera (art museum), the Science and Technology Museum, and Basilica of Sant'Ambrogio. If you're interested in design, fashion, and/or shopping, there is plenty you would enjoy in Milan. Brera and Naviglio Grande (Grand Canal) are two great areas to walk around in. Lots of great restaurants there.