My wife and I were in Milan for a couple days last month.
Peck
I couldn't agree more with the recommendation for Peck. It's a food lover's paradise. In the basement they have an extensive wine cellar with a tasting room, on the main floor is a grocery store with tons of packaged specialty items and interesting prepared foods, and upstairs is a chic coffee shop. The coffee shop features coffee beans from all over the world including the fascinating
kopi luwak which is digested by an Indonesian civet before being dried and roasted for consumption. I didn't try it because it was pricey, but pretty cool nonetheless. Peck is a great stop to pick up gifts since they carry many interesting food items.
http://www.peck.it/Princi Bakerypictured: ricotta foccacia

Princi Bakery (it has four locations in Milan and one in London) is everything you're looking for in an Italian bakery. The atmosphere is elegant and all the breads and pastries are baked fresh every morning. We stopped by a couple times to pick up some pastries and a cup of coffee. I particularly loved the foccacia that was spongy and substantial and brushed with delicious olive oil. Definitely a worthwhile stop.
http://www.princi.it/Pizzeria Spontini
Pizzeria Spontini is one of those places that makes only one thing, but makes it extremely well. We got there about 10pm on a Friday night and the place was packed with people popping in for a quick slice. This is a grab and go operation, and the pizzas are coming out of the wood-fired oven about 2-3 per minute. They slice them up and throw them on plates and the line of people buys them as fast as they can plate them. The crust is spongy and soft and can barely support the thick layer of gooey cheese on top. I didn't get to sample much pizza in Milan, but this impeccable slice was all we needed.
http://www.pizzeriaspontini.it/Buon Gustopictured: pastas stuffed with mint and fava, pecorino, and buffalo mozzarella

This was a pleasant discovery as we were walking around looking for lunch on a Saturday afternoon. From our limited Italian, we worked out that the sign in front meant hand made pasta, so we figured it was worth stopping by. The server was enthusiastic about practicing his English so he told us all about the different pastas they had available. He stressed that the pastas change with the seasons. From what I could tell, it seems they primarily do catering and ship pasta all over Europe. The room is more an informal cafe where you order from the glass counter and have a quick bite with a glass of wine. The pastas were exceptional across the board. He served us a sampler of three different pastas he considered to be particularly fresh that day. I liked that each pasta was topped with a different sauce, always simple so as not to mask the flavor of the eggy pastas and delicious fillings. This was a great find.
http://www.buongusto.eu/Cioccolati Italianipictured: hazelnut and dark chocolate gelato

We were particularly lucky on this day (though I think Milan may just be a kick ass food town). After we walked out of Buon Gusto, just around the corner was a bustling gelato shop named Cioccolati Italiani. Unlike many tourist gelato shops, the gelati are stored in metal containers so you can't see the colors and flavors. Instead you pick from a list of flavors. They fill each cone with your choice of white or dark chocolate. I particularly enjoyed the hazelnut, but all the flavors we sampled were excellent.
http://www.cioccolatitaliani.it/Da Abelepictured: truffle risotto

It's a short metro ride from downtown to get up to Da Abele, but it's worth it for the interesting risottos. Every day Da Abele features three risottos that use seasonal ingredients. Naturally we ordered all three. All the risottos were perfectly creamy and al dente, no surprise since everyone is ordering them. We also ordered a couple antipasti, which were good, but paled next to the superb risottos. The three risottos were zucchini with olives, salted fish roe (called bottarga), and truffle. I liked that they were simple such that they underscored the ingredients and the texture of the risotto. Definitely worth a visit.
Via Temperanza 5
20127 Milan
Ratanapictured: risotto milanese with osso buco

A friend of mine spent a month in Milan last year and told me that if I wanted traditional Milanese cuisine, I had to visit Ratana. So we got a reservation and headed up there. It's not far from the happening Corso Como/Garibaldi area, but it's completely off by itself. From the street it looks like a local government building or something with a gated door and a park (complete with swing sets) in front. We started the meal off with an order of zucchini and shaved parmesan cheese and house smoked veal. The zucchini was sweet and delicate, balanced nicely with a creamy olive oil. The veal was tender and served on a bed of crunchy arugula and topped with ripe cantaloupe. Just about everyone in the room was ordering the special osso buco with risotto, so we followed suit. The osso buco was fork tender with a big beefy flavor and served in a hearty stew. The saffron risotto was creamy and rich, pairing beautifully with the osso buco. I can't imagine how this dish gets any better than that.
http://www.ratana.it/From Milan we headed to
Venice.