Children are very well received in Madrid restaurants and generally treated like small adults. All over the country -- and perhaps nowhere more than Madrid -- the perception and tolerance of noise is quite different from that of North America and Northern European countries. (Madrid is said to be the second noisiest city in the world. After Tokyo!) Thus, as a rule, children have to be spectacularly loud for anyone to even pay much attention. Child-size portions of dishes are available in most eating spots and priced accordingly. Dining out earlier would certainly avoid the crowds but Spaniards don't particularly bother about this and it's not unusual to see young children (down to 3 or 4 years old) eating with their parents as late as 10 or 11pm. However, this en famille trend is less common in the pricier and more upmarket restaurants.
Children will delight in patronizing any of the restaurants at the Parque de Atracciones in the Casa de Campo. Another good idea is to go on a picnic.
For a taste of the familiar, Madrid has several fast-food chains: Dunkin' Donuts, McDonald's, Burger King, and KFC are everywhere. Remember, however, that the burgers and chicken will have a slightly different taste from those served back home.
A place with juicy hamburgers, plus lots of fare familiar to American kids, is Foster's Hollywood. Or try taking the family to a local tasca, where children are bound to find something they like from the wide selection of tapas.