I'm going to focus on western medieval Europe here, although sadly that scope eliminates things like princesses running international spy rings to expose traitors or emperors transforming into a demon.

The practice of governance in the west changed a lot over the course of the Middle Ages. Two changes in particular affected royals' daily life. The first was the rise of bureaucracy, creeping slowly upwards until the 12th or 13th century when it really took off.

The second was the dominance and slow decline of "peripatetic" government--that is, "moving around." The entire royal court would up and haul from lord to bishop-lord to lord to city and back. Early and high medieval chronicles from Germany are filled with "The king spent Christmas at Augsburg and the New Year at the palace of the bishop of Trier and in March he created Eberhard as bishop of Bamberg at that palace."

The point being--for much of the Middle Ages, kings spent a lot of their time traveling! The situation is more ambiguous for queens. We see plenty of queens regnant in the late Middle Ages, mostly of smaller principalities, so both time and place made their governments much less peripatetic. It's not always clear from chronicle accounts whether queens consort were travelling with their husbands, and in many cases, we'd expect not. Some definitely did, though. Violant of Bar, queen of Aragon around 1400, is a great example--she even had her own perambulation to her own palaces, met with her own governing councils...bordering on "co-government" with her husband.

But royals couldn't be on the road or leading armies 100% of the time. When we look at daily activities, it's important to keep in mind that kingship and queenship were more than listening to advisors and making decisions. "Political culture"--rituals, appearances, relationships--was almost or even equally vital to political power and governance.

The first and most important part of keeping up appearances was religion. Regardless of whether royals were pious, they had to appear to be. Queens consort in particular were expected to spend a significant portion of the day at prayer, and kings seem to have done so as well. Many of the most elaborate prayer books of the late Middle Ages belonged to royalty, like Queen Elizabeth of York's Book of Hours.

Attendance at Mass could also be important. Special Masses were an important occasion for crown-wearing by the reigning monarch--a show of power.

Activities like hunting or falconry also occupied monarchs' time. It was probably partially fun, at least for some kings and queens; it was probably also a time when court members invited along could gain an informal ear. But even more, it was just a time to cement relationships. This was especially important in the days of peripatetic kings. The major reason for the ambulatory court in the first place was to bring the ruler in contact with princes (high nobility).

There was time for what we would consider more traditional governing activities as well. Christine de Pizan describes King Charles V (not that Charles V) discussing affairs with his royal council on a near-daily basis, although her picture is an idealized one for propaganda purposes.

"Paperwork" was another joyous occupation. That might just mean giving approval to charters transferring land. But queens like Margaret of Anjou also spent a good amount of time reading and writing letters, involving herself as mediator in complaints between tenants and landlords or among petty nobles.

And uniting the idea of relationship-building with governing, there would be ample time to receive visitors and hear petitions formally and informally. When Duchess Kunigunde of Austria was princess of the Holy Roman Empire at the end of the 15th century, she often acted as mediator between visitors and her father. That would be a great example of time for informal meetings, since in general ruling monarchs were not "supposed to" (appearances again) spend time with their families.

How much time queens consort spent with their children probably varied a lot. Scholars usually stress queens' interest in their children, although that could mean overseeing their education from afar. Our letter-writing queen, Margaret, also wormed her way onto her son's advisory council while he was being educated away from court. I can't think of reading anything about princes consort as fathers, or really that much at all. (It was probably in the interest of queens regnant to keep their husbands as much out of the spotlight, and thus the sources, as possible.)

Meals offered another chance to display, exercise, and award power. In the queen consort's apartments, for example, which ladies-in-waiting were granted a place at the queen's table for any given meal was a big deal. The privilege to serve the queen her food was even more desirable. And that was just "private" dining! Major feasts and parties were not necessarily a daily activity, but they formed an important part of royals' lives. Observers like Hans von Planitz, representing Frederick the Wise at 1520s Reichstag conventions, even relate to their noble or royal employers who the best dancers are--to relate "what people are saying" as important state information, not just fluffy gossip.

Finally, there would have been time for what we would consider "leisure," although it might overlap with other purposes. That could include things like going for walks in palace gardens, playing chess, listening to books or reading them firsthand, playing with pet dogs.

Especially playing with pet dogs, and in the late Middle Ages, especially little white fluffers. The story I'm going to tell comes from 1709, which is not the Middle Ages, and from a letter by the Duchess of Orleans, who is not technically royal. But it well illustrates the importance of puppers in medieval and early modern royal life (and also, it's the best primary source on the Internet):

One of my little dogs has just jumped up on the table, seized my paper and torn a word, as you see. The lady who did this fine trick is called Candace or Robe, which latter name was given to her because her mother Charmille had her puppies on my robe.

The Princess was with me, and we were seated on a sofa chatting together, when Charmille, who was behind me, began to whimper and fidget as she always did when she wanted to be caressed. The Princess said to me, "Your little dog is restless, what is the matter with her?"

I said, " She wants me to stroke her." I put my hand behind me to pet her, and felt it all wet, she had just had her puppies on my gown, which was spread out all around me.