I’m not a fan of Milan, so I would probably spend no more than 2 nights at the beginning or the end (a car is not recommended while staying in Milan, as it would need to stay parked in an expensive garage the whole time).
Christine suggested Stresa on Lake Maggiore, which is very close to the airport. I second the suggestion, and since there is so much to see in that area (Borromean islands, Lake Orta, Orta San Giulio, Cannobio, Locarno, Cento Valli scenic railroad, etc), I would probably spend 4 nights in Stresa.
A car for lake Maggiore and lake Orta wouldn’t be a bad idea, but it is possible to use only public transportation (buses, trains, ferries).
The list is really endless of other locations you might want to consider:
Langhe and Monferrato (wine country) of Piedmont
Val d’Aosta, Mont Blanc, and the Alps in the region
Lake Como, north of Milan
etc.
Also many interesting cities are in northern Italy besides Milan, such as:
Turin
Bergamo
Parma
Bologna
and so on.
Obviously cities, like the ones mentioned above, are best done without having a car, which would be a very expensive hindrance. So if you include cities in your itinerary, as well more rural/lake locations, try to concentrate the car rental days for rural areas and the no car days for the cities separately. For example you could start with the city of Milan, then take the train to Turin, and visit Turin for a few nights, then rent a car in Turin and head to the areas where a car is more useful (wine country, lake Maggiore and Lake Orta), and finally return the car to the Malpensa airport before flying home.