Milan airport to Duomo area by train?
 

We are flying into LIN and we're hoping to take a train to our hotel area. Suggestions? Thanks.

You can take a train, the Malpensa Express, as far as Milan Central Station. Then you can take the metro, the yellow line, direction Peschiera Est, four (?) stops to the Duomo stop.

Sorry, I just saw you were flying into Linate. I've never been there, but the metro now serves Linate airport. You'd have to change trains at Crocetta, taking the yellow line, direction Comasina, for two stops.

Thank you. Any suggestions for a round trip private transfer from Linate to city center hotel?

If you want a private transfer to your hotel I would presume you are staying at one of Milan's 5 star hotels. If so the hotel would be able to arrange this for you.

Otherwie use the taxi service at the airport (white cabs). Linate is a city airport so the transfer to the city center hotels is quick and reasonably priced.

Yes, simply go outside and get a cab. They are going to be there; Linate has a relatively small terminal and the fare to your hotel probably won't break the bank.

All true. A taxi ride is quick and inexpensive from Linate.