Shopping with a one-year-old is challenging. You must time his meal and nap meticulously so that you can shop while he sleeps in his stroller. The Mitsukoshi Department Store in Ginza did an entire makeover last year and is now very baby and mother friendly. They have a great outside garden on their rooftop where kids can run around and play (and get tired). Restaurants in the department store are also baby-friendly. The thing about Japanese department stores is the quality of the restaurants in them. It's not just a regular food court like in the States. They have 10-15 restaurants in all types of cuisines, and in all levels from fine-dining to cafes.
We had lunch at Minoru diner, a Japanese food cafeteria. They had a salad bar with all sorts of Japanese vegetable dishes, which was perfect for Yuuki and I.
After lunch we had gelato on the rooftop garden, and Yuuki ran all over the place he fell asleep on his stroller, giving us about an hour to shop: )!