So, you're right to say that itinerant rulers was far more a feature of the Norman and Angevin dynasties (so, the eleventh through thirteenth centuries) than it was for the Tudors. The reasons for this difference are many, but I'll try and give you a few (honestly, the movement of monarchs is the subject of many books, such as An Elizabethan progress : the Queen's journey into East Anglia, 1578, Zillah Dovey). Unfortunately, I'm only really able to answer with specific reference to England.

So the first important difference is that Norman and Angevin rulers were in control not only of England but of Normandy and surrounding parts of France; the administration of the two realms was effectively separate, and (along with the fact that early rulers up to Henry I appear not to have spoken any English) most of these monarchs spent over a third of their time in France. We may contrast this with Henry VIII, who (to my knowledge) was only in France for a few major occasions (His first war with France, the Field of the Cloth of Gold, the introduction of Anne Boleyn to the French King, and so on); France was, in other words, no longer subjected to regular royal visits, even though the King was obsessed with its "return" to England. This can of course vary between monarchs; in the eighteenth century, for example, George I would spend a great deal of time in Hanover, the province of his origin in modern-day Germany.

Just as important, however, is the fact that England of the 16th century was a more settled (though by no means entirely peaceful) kingdom to be ruled. The Tudors had carried out an extensive and ruthless dynastic purge (the last wave of which took place in the 1530s and 1540s with the execution of figures such as Margaret Pole) and the net result was that there was rarely a reason in military terms for the King to leave the capital (especially given that he delegated much of the business of defending the Northern marches to Northern aristocrats, and indeed delegated much of the business of generalship in general). This can, of course, be contrasted both with the Wars of the Roses and with the Civil War; in both cases, unsurprisingly, warring monarchs proved to be particularly itinerant.

It is also worth considering the ways in which the nature of a Royal progress changed over the period. As I've already mentioned, Elizabeth's royal progresses are the subject of considerable study (as another aspect of the ways in which a Queen could express her authority in a gendered world); but it's worth noticing that even Elizabeth's progresses rarely left what we'd call the Home Counties today - indeed, Elizabeth never went on a progress in the North over the forty-five years of her reign. In one sense, a Royal progress was a sensible method of allowing refurbishment of royal palaces and an escape from London, usually in the summer; but it was also a way to enjoy the hospitality of a lord, usually at ruinous cost to that lord (while we can only estimate the costs of a Progress, it is easy to see the extent of their expense from accounts such as that of Elizabeth's three week stay at the home of her favorite, Robert Dudley, at Kenilworth Castle in 1575). Royal progress was always a way to express power and extent patronage; but increasingly, nobles found their way to the court, as opposed to the court coming to them. While Norman noble families had often attached their sons to the Royal court (the positions these sons played, such as that of a 'Royal baker', would eventually evolve into the Royal Household), Early Norman rulership was that of a very small minority; it would not have been possible to rule from the distance of court, especially when that court was itinerant. The ultimate result was that the nobility of the eleventh and twelfth centuries was far less prone to travel and that of the sixteenth far less restricted to their own land.

Finally, it is also worth noting that the process of administration had not only become more centralised by the sixteenth century, but it had also become more estranged from the figure of the King himself. While the monarch could involve themselves extensively with Royal administration - and, indeed, Elizabeth appears to have made every effort to do so - they did so largely in London, through offices such as the Privy Council and Parliament, to differing extents. While Norman and Angevin rulers certainly had various methods through which to enact legislation and to express their will (such as writs and charters, as well as later innovations such as Pipe Rolls) both the size of administration and its centralisation were very much different; indeed, the financial capital was in Winchester and Norman records were kept in France, separate from those issued in England.

This is really only a minor comparative list, and I honestly couldn't hope to give a comprehensive answer on the topic, which is very broad. You might also try (as well as general books on each period, which will always cover this topic in some detail) Michael Clanchy, From Memory to Written Record, which is about the growth of this administration and is also a pretty decent read!

I was asked to give an account of the Italian situation since society in the peninsula was quite different from the rest of Europe. Much of my discussion will be primarily limited to northern Italy as the Kingdom of Sicily is a completely different animal.

Italy is unique in terms of the persistence of urban settlement during the post-Roman period. While it is undeniable that quality of life and the maintenance of civil structures certainly went down-hill after 476 (as well as before it), urban life was so ingrained in Italian society that the Lombards who settled in the region felt the need to at least maintain cities homes in cities, even if they preferred to live in the landed estates outside of the city. Indeed, Italian poets were still writing civic panegyric in the depths of the post-Roman economic depression. Cities maintained their allure as vital cultural centers that forced the nobility to pay attention to them.

The importance of cities in Italian culture rested on the fact that they were more than administrative centers. As Adrian Verhulst has pointed out, building on the work of Hodges, the great commercial cities north of the Alps emerged "organically" and oftentimes were not strongly Roman. This is because in many cases, Roman cities in Northern Europe functioned as administrative centers rather than lively centers of urban life. This is of course a gross oversimplification, Cologne, London, and other cities certainly had strong Roman roots, but Verhulst's argument is that for the most part, Roman settlements did not sink roots into the local culture, particularly northern Gaul. We can talk about emporia and the emergence of other urban agglomerations north of the Alps in another thread.

This trend continued throughout the Middle Ages. While many nobles maintained estates in the countryside, especially during periods of German occupation (Frederick Barbarossa and his ill-fated successors). These local nobles often played an important roll in urban politics. Take Caffaro di Rustico, the civic chronicler of Genoa in the early 12th century. He was the lord of Caschifellone, a region north of Genoa, but it is clear from his career, he made his primary focus the city.

The presence of nobles in cities could become problematic for the other citizens. Nobles clashed and vendettas (literally) that got out of hand were a frequent concern of Tuscan chroniclers. There is an excellent example of this from 14th century Siena in the reader, Medieval Italy: Texts in Translation, edited by Jansen, Drell, and Andrews.

These clashes could get out of hand and noble families would often build towers to defend their position within cities, with San Gimignano as the classic example (http://www.casagirasoli.com/wordpress/wp-content/uploads/2013/11/cosa-fare-a-san-gimignano-ok_Snapseed.jpg). The struggle between noble and popolo power was often manifest in legislation about the height of these towers such the law passed in Florence that stated that no private tower could be taller than the Palazzo Vecchio.

During the period of the Signoria, (second half of the 14th century-15th century depending on the city) when individual strongmen ran the affairs of cities, these individuals often ruled from fortresses in the city, such as Sigismondo Malatesta's Castel Sismondo in Rimini.

This is pretty brief and there's a lot more to be said, but I'm tired.

I think I'd approach this question somewhat differently than the other answers here, which is identifying change over time (here the medieval period) in law, related government administration, and the function of nobility.

I might summarize it like this: where nascent nobility warred with one another from the beginning of the high middle ages, by the late middle ages they were suing each other in court. And those courts were by and large located 'near the the king'. We can see here how the notion of 'court' in terms of nobility and kingship, and then the 'law court' are related.

While by the time of the late middle ages it was infrequent that the king of either France or England were involved in daily trials, whether criminal or civil, the trials were held in their name. This could be the various strata of English courts, ie Court of Common Pleas, Court of King's Bench, etc, or French equivalents like the Parlement. These courts, which were the highest appellate courts, heard pleas of the nobility, and they were at first travelling with the king while he and his advisors ruled on disputes of the aristocracy and some, likes the Assizes of England, travelled in their own circuits in the King's name. They came to fix themselves in/near London or Paris respectively in the 14-15th centuries, developing regional 'sub-courts' still in the name of the king.

Jurisdiction of these courts was overlapping and confusing particularly in France where there was the development of a civil code (effectively for nobility and serious cases) alongside the costumes or local laws which had been passed down orally over centuries an finally documented in the 13-14th century.

Beyond the growing legal centralization, there was also the development of advisorship to the King (estates generale) or nascent parliaments such as that provoked by the Magna Carta. These would require the upper nobility to attend the court of the King.

All of this meant that (in the longue durée) the requirements of nobility hewed to the needs of the formation of strong legal and administrative states. Nobility could travel more not only because they needed to (ultimately because their assent to the King's authority in law and administration), but the infrastructure for administering their own estates was more assured through the late middle ages with the replacement of personal bonds with bonds of duty, responsibility and 'professionalism' such as provosts, bailiffs, sheriffs, seigneurs, judges, etc.

If we contrast the period of the 10-13th centuries, nobility in France and England would have been greatly preoccupied with the functioning of their estates including warfare, farming and expansion of assarts, development of towns which sprang up at the behest of lordship, personal administration of local justice, and spend time with other local lordship/peers in their own conflict resolution councils.

Going back further, we can contrast Carolingian rule in the 8-9th centuries and find a different interaction: while kingship was central and required the counts and dukes to attend placitums to advise the king and solve disputes among nobility, and to plan war-based expansion at the borders, the nobility were granted by the king the right and duty to hear cases of disputes among their freemen on behalf of him. But the nobility at this time was far more mobile as well, leading a pre-castle life of shifting with the needs of agriculture and external conquest.