Until the reign of Charles V, there was no such thing as a capital. In other words, the capital was where the king was, and the monarchs were very much itinerant. This one can see just by reading the datum of documents produced by the Royal Court, like documents emanating from the General Registry of the Cort's Seal or the Chamber of Castile. King Philip II, among the first things he did, was to decided that the Royal Court should be in a fixed place, not only for his own commodity, but also for the convenience of the functionaries who would not need to be constantly travelling. As for where should he settle, he had a number of options.

Seville was the most populous and richest city, but it was too far away from other important places like Barcelona, Valencia, or the northern ports.

Toledo was a very centric city, and very rich. The main problem was that it was under the jurisdiction of the archbishop of Toledo, so having the court not in a place of royal jurisdiction would be a big no. A King having no authority over the city where he resided would have been completely unseemly, as the Crown's authority could be hindered by the archbishop of Toledo

Valladolid would be far from Seville, Valencia, and Barcelona. It had the advantage of being of royal jurisdiction, but the disadvantages outweighed the advantages.

Madrid was very centric so the information from the limits of the country would be received relatively soon from any given point, it was a place under royal jurisdiction, had a very good supply of water, and there were top-notch hunting places in close proximity, something the king loved. The fact that it was a rather small place (12,000 people) played in Madrid's favour, as there were not any really strong local powers, so the king's authority would not be hindered by nobiliary disputes. Thus, the rank of capital city was bestowed or maybe thrust upon Madrid.

As I mentioned, Madrid's supply was very good, and it was perfectly adequate for a town with a population of about 12,000 individuals. However, with the town becoming capital of the kingdoms of the Spains comes population growth, in this case an absolute population explosion.

Madrid not only had a river, small as it might be compared to the great rivers like Duero, Tajo, Ebro, or the mighty Guadalquivir, but it also had some streams, like the Abroñigal, and a network of qanats dating from the Umayyad period that could guarantee the supply of water.

The population kept growing, to the point that the water supply became compromised, so in 1608 the Board of Waters of Madrid (Junta de Aguas de Madrid) was created as an independent organism that would be in charge of guaranteeing Madrid's supply of the element of life. And the Board delivered.

Five "viajes de agua" (water canalisations from streams and aquifers) were created: Buen Suceso, finished in 1618; Amaniel, completed in 1621; Fuente Castellana, in 1620; Abroñigal Alto, and Abroñigal Bajo, in 1630 both. As the city kept growing, more viajes were built: Contreras, done in 1645; Alcubilla, 1692.

So, lacking an impressive river, the city and the Crown had to make do with what there was available in terms of rivers, streams, and underground aquifers in order to have a strong water availability in the town.

Am curious, did the Romans have any important settlement or city in Madrid?