In Spain, the itinerant Court stopped with King Philip II, in his early reign. In order to have a more stable administration, he chose a place where the Court would stay in a stable manner. To be precise, he chose Madrid, still the capital of Spain.

As for why he chose Madrid when there a number of larger and more prestigious cities, the exact reasons are unknown, but the choice makes sense. Madrid is nearly the geographic exact centre of the Iberian peninsula, which is a good thing, being as far away from the Northern ports (Santander, Bilbao, San Sebastián) as from the Southern ports (most notably Seville), and somewhat closer to Valencia: this allows the King and the Court to be reasonably well informed.

It still leaves the question on why he did not choose Toledo or Alcalá de Henares.

Toledo was a city of ecclesiastical jurisdiction, belonging to the archbishop of Toledo, primate of the Spains. This would have been a great problem, as the King would not be the actual authority in the Court's city, diminishing his nominal and actual power.

Alcalá would have been a perfect choice as it was a culturally important city with a very prestigious university, which could have given the Administration a steady supply of highly qualified civil servants and jurists. Alas, Alcalá had a mighty big problem: it was an important centre of the printing business. This may seem like a good thing, but it wasn't. Alcalá had had a couple of prominent protestant groups, lead by Brocar and Miguel de Eguía, printers. Other important protestant cores were Valladolid and Seville (see autos de fe of Agustín de Cazalla and Constantino Ponce de la Fuente), big cities with or close to large printing firms.

In Madrid, with a population of 12,000, Philip II could start a capital city anew, free from ecclesiastical or nobiliary jurisdiction, and devoid of protestant shenanigans. And so he did.

I see there has already been an answer put forward but I thought I’d talk specifically about Versailles as well, as this is the example you mentioned.

The construction of Versailles certainly marked the end of the peripatetic nature of the French court. When Louis XIV officially relocated the court there in 1682, it remained the main seat of the king until the royal family were forced to return to Paris in 1789. This change came about as a result of the building of Versailles, as even Louis himself moved around from estate to estate at the start of his reign.

While the general view is that Versailles was built as a glorified birdcage that would allow Louis to keep a watchful eye over the nobility, this isn’t strictly true. It’s certainly a fact that the nobility living at Versailles were carefully observed, however the palace could only house 4000.

While this sounds like a large number, one must consider the fact that the French aristocracy of the 17th Century was monstrously huge, consisting of tens of thousands of individuals. This, paired with the fact that many chose to live away from Versailles when problems with sanitation, accommodations etc became obvious in later years and the fact that Louis himself lived away from the palace, staying instead at the Grand Trianon most of the time in his later life, makes it seem unlikely that Versailles was effectively used as a way to spy on the nobility.

Versailles was envisioned by Louis as a way to modernise the French court and to stand as a monument to his magnificence and gloire (glory). He ended the movement of the court between provincial estates and instead had guests come to him in a vast display of the beauty and wealth of French culture.