First time travel to Tokyo, Small group, 4 ppl and a baby 1yo, best location to stay in Tokyo?

One week trip, plan to spend the whole week in Tokyo, our itinerary so far only shopping, near by temple and culinary, try to make it easy with a baby. I checked Akasaka, Shinjuku. Im confused with all the options. So far I found a quite apartment in Shinjuku city, but wonder of there's a better option. Tia