Most attractions at Madrid are at walking distance from one another. When you are travelling with children, make sure to stay at city centre.
There is no need to purchase ticket in Madrid public transport for children under the age of 4. For older children, you can buy a Children card.
Newer metro stations are more child-friendly than the older ones. However, if you are travelling with an infant, you will not have too much difficulty in using Madrid metro or bus.
Strollers are allowed on Madrid buses and metro trains. In the older parts of Madrid, the sidewalks are very narrow making it difficult to maneuver strollers. Luckily, the most important ones are pedestrian friendly making it that much easier.