Skip the limoncello, or buy it at the airport duty free if you really want it.
A few things I almost always bring home from Italy include:
High quality tinned or jarred tuna packed in olive oil
Bottarga, if you like the taste. From Sardinia, if possible
Olive oil, but only in the fall after the new oil is on the market shelves; NOT with truffles!!!!
Dried pasta but only if its from a top maker like Martelli (from Tuscany; look for the yellow bag) or one of the artisanal makers from Abruzzo,, Puglia or Le Marche
Maybe some good quality flavored olive oil like orange flavored
Colatura, from Sicily or Cetara (great ingredient in cooking; made from anchovies; very pricey outside italy)
Mostarda from Cremona (easy to find in Milan)
Chocolate from Modica, Sicily, also should be easy to find in Milan and a grainy chocolate similar to that made in Mexico...in dozens of flavors
High quality rice from Lombardy, like Vialone Nano
Taggiasca olives from Liguria, or others that you like--try to find these vacuum packed
Hazelnuts, vacuum packed, from Piemonte
Pine nuts (keep in fridge at home). Make sure these are from Italy!!
Dried porcini; also make sure of country of origin
Barratii and Milano candies from Turin, or similar made in Milano I don't know any names, but NOT Perugina!
CHEESES......all except very fresh cheese, which does not keep well
AND...if you are not from the USA: Salumi!!!!!!!
The list is endless and I'm sure I've left out a lot of stuff!!
If you plan to do a lot of food shopping, bring bubble wrap and a roll of tape from home for secure packing. (Hotels will often help you pack and give you a carton that you can use as a checked item on the place; remember that you can also ship your items home from Milan)
Not all of these are from the north, but should be easy to find at Eataly or in small specialized food shops.
I've brought home a lot of olive wood small table items and salad bowls but these are no longer inexpensive.
Also, one of those gadgets to toast bread for bruschetta (hardware store)
One thing not to buy: Those multi-colored dried pastas sold in tourist shops. They do not look so pretty when cooked and are not usually made with the best quality ingredients...
Scented bath/beauty products such as those from FARMACIA SANTA MARIA NOVELLA (see if they have a shop in Milan), AQUA DE PARMA, ORTYGIA....if you like those scents
Not food, but in Milan: LEATHER GOODS from the fine designers, some with no outlet outside Europe!!
And remember the VAT refund that you are entitled to!!! It can amount to a lot of money back!!! Just make sure to bring your passport when shopping.