One option that exists in almost every city is room or apartment rental sites directly with the owner, such as Airbnb. In this mode you that are travelling with children will probably get a kitchen option to prepare the food for the little ones.
You can stay in a place just for you and your family or rent one or more rooms inside someone’s home, usually an American. This experience is interesting for the exchange of information and even tips that the resident can give you, but at the same time if you are with children and they usually “strange” who they do not know very well may be a little confused because they are living with other people for a period.
It is worth analyzing the behavior of your children and which option best fits your family profile.