Look into the Tokyu Stay chain. They aren't luxurious, but the last time I stayed at one, there was a family of four actually living there until their expat apartment was ready. You'll have a kitchenette and washer-dryer in the room, along with Internet connections.

Oh, and get a map of Tokyo so you can see where the places you want to see and the hotels are located. The transit system in Tokyo is so fantastic (and most kids enjoy riding trains) that you can stay pretty much anywhere in the central city and not be too inconvenienced, but if you have read in your guidebook about certain things you definitely want to see, try to stay either near those or on a train line that will require as few transfers as possible.