Where to stay near Malpensa airport

There is the Sheraton across the terminal T1 (if your budget allows).
My budget prefers lower prices, so I always stay here when I fly to/from MXP:
http://www.cavalieridellacorona.com/en/home-page.aspx
Generally I have a car, but if I’m flying out in the early morn I prefer to return the car the evening before then take the hotel shuttle back to the hotel. The hotel shuttles stop near the exit 10, (north end of T1) if I recall correctly.
If you are picking up a rental car, you can do so upon landing, then drive to the hotel yourself (5min) or use the hotel shuttle to go back and forth and pick up the rental car at the airport the next morning. Your choice. If you use the train, the station is across the T1 (under the Sheraton).

We've stayed at the Sheraton several times. Especially coming in late from the West Coast jet-lagged, it's been very convenient. Next morning we grab the train into Milano Centrale and continue our travels.

I stayed at the Sheridan on my way to US and coming back. The train station very close to the hotel entrance for the next morning. Seems prices vary widely based on availability. I lucked out and both nights and rates were around 125 €. There are also hotels near the airpirt that have shuttles, or just take the train to Milan Centrale and stay someplace close to the station.

One of the Marriott chain hotels is right at T2 and pretty inexpensive.

The Sheraton is the best choice, if your budget will allow (it's somewhat posh). The hotel is connected to the terminal so you can walk right from the lobby to your departure gate.

The hotel that JerryG mentioned is the Moxy. It’s a fun, very modern hotel. I stayed there the night before flying home from Malpensa. It was very handy and a good price.