My point is that you don't necessary use same airport.Going back to Kanasi only to fly out is a waste of time.Take it into consideration,when you book your flights.
In general,Families can stay in youth hostels which have private rooms.but not always they have.
If you really want to stay,check this and ask them.
Japan Youth Hostels, Inc.
If you don't mind staying in dormitory, youth hostels might be cheapest.But if you want to stay in private rooms,they are not always cheapest.Try "business hotels".