Is there any historical documents or autobiographies of what it was like being a king?

I immediately thought of the "political last wills" or "political testaments" that have been written by various rulers throughout the ages. Depending on the individual text they fluctuate between self-justification, political autobiography, philosophical musings about the nature of monarchical rule and recommendations/suggestions for their respective successors. Most of the examples I am familiar with hit all four of those to varying degrees. I'm haven't read yet any scholarship that tries to take a general look at those testaments as a genre, however, so I can't really comment on anything they might have in common. I'll quote short excerpts out of three early modern examples, however, which I feel show well what these documents' intentions were and what you can find in them.

Meine Gedanken (My Thoughts) by Duchess Anna Amalia of Saxony-Weimar and Eisenach, c. 1758. Anna Amalia was only eighteen years old when her husband's sudden death forced her to take the throne; she wrote the following shortly afterwards:

When I look back at my childhood, that springtime of my life, what do I see? An ever-recurring round of sacrifice made for others. I was not loved by my parents, who on every occasion kept me in the background, my brothers and sistes being always considered first. I was treated, in fact, like an outcast, and yet Thou, O my Creator, hast endowed me with a sensitive, loving heart, which suffered misery from this want of tenderness and pined for affection. I was starving for love, and I reveived the hard crust of mere duty. [...] Never did I pray with such devotion as I did in this my hour of need. I believe I might have become a saint. The situation was indeed peculiar. So young to be regent, to command, to rule, I, who all my life had been humiliated, depressed. I am afraid that after a little time I began to look upon my position with a certain amount of vanity. But a secret voice whispered: "Beware!" I heard it, and my better reason came to help. Truth and self-love struggled for the mastery, and the truth prevailed [...] I longed for success - for praise. I also felt the absolute need I had of a friend, in whom I could place entire confidence. IThere were several who sought to be my confidants or my advisers. Some tried flattery, others commended themselves by a show of sincerity, but in none could I detect the ring of true affection which is above all temptations. If a prince and the individual he selects as an intimate or confidant are both noble-minded, the sincerest affection may exist between them; and this is the only way to answer the question, "Can kings have true friends?"

Archduchess Maria Theresia of Austria wrote her political testament at about the same time, but her situation was very different. She took office in 1740 after her father's death when she was 23 years old and almost immediately found herself embroiled in a series of devastating wars which directly threatend her realm's very existence. Eighteen years later she put some of her thoughts about that crisis to paper (translation is mine):

Out of motherly care and for the benefit of my posterity written Points of Instruction, which I divided in various chapters depending on their importance.

The first chapter is to describe the domestic and foreign political state of the monarchy, as I found it to be when I began my rule.

The second describes the abuses which gradually built up in this Austrian monarchy under the rule of my ancestors.

The third chapter deals with the nine year long and burdensome war and why I decided to eventually bring it to an end.

The fourth tells about the changes I effected at court and in my realm after said peace.

The fifth shows the great benefit and use of those changes, as those are the only way to strengthen the monarchy and keep it for my successors.

The sixth chapter describes the necessity to keep those changes in order to avert your own downfall, and what my successors should pay attention to to that end.

The unexpected and sorrowful death of my father was that much more painful for me not only because I venerated and loved him as a father, but also because I saw myself as his lowest vassal and him as my lord and ruler and therefore felt twofold loss and pain. Back then I lacked the experience and knowledge to rule this large and widely spread realm, since my father had never thought to involve me in the domestic or foreign policy of his or at least inform me of it, and so I suddenly and all at once found myself bereft of money, troops and good counsel.

[She goes on to tell in great detail of how dependent she was on the counsel of the ministers she had inherited from her father, and how lacking she found it in many aspects, and then proceeds to the next chapters]

Sixth Chapter

[...] I can give my successors no other advise than to not let themselves be led into confusion, as many advisors are in fact led by their own interests. I myself would have been led astray while implementing aforementioned changes due to so many interjections and news if I hadn't taken great efforts to learn about and truly understand the affairs myself; for this reason I find it necessary to ask my successors to not change anything about the changes I implemented and instead protect and conserve them for the best of the monarchy and for its continuing existence. To that end they should especially pay attention to find honest and qualified people as well as teach young people so that those can learn about the affairs of state themselves and will be able to faithfully serve the prince and the people, and to do so well.

And the last one is a short excerpt from the political testament of Maria Theresia's greatest enemy, King Frederick II of Prussia who was the first to invade her realm not even three months after she had taken the throne. Frederick wrote this testament in 1752 and again rewrote and extended it in 1768 (again my translation).

Every citizen's foremost duty is to serve his fatherland. I tried to fulfill this duty througout my life. As the person with the highest authority in the state I had the opportunity and the possibility to make myself useful for my fellow citizens. My love to them instills in me the wish to continue serving them even after my death. But I am not so arrogant as to think that I myself should be the only ideal my successors should try to emulate. I know, that death destroys man all as his plans, and that everything in the world is subject to change. With this political testament I only try to tell my experiences to those who follow me, akin to a captain who knows the stormy areas in the sea of politics. I shall detail the cliffs which are to be avoided, and the harbours where my successors can find safety. [...]

Amongst all provinces in Europe there are none which would be a better fit for our state than Saxony, Polish Prussia and Swedish Pomerania, as all three would fill the gaps in our borders. [...] [Polish Prussia] separates Prussia from Pomerania and prevents us from protecting the former due to the difficulties provided by the river Weichsel there, as well as the possibility of Russian attacks via the Danzig harbour [...] I don't think that war would be the best way to add this province to our kingdom, and I tend to tell you the same what King Victor Amadeus of Sicily told Charles Emanuel: "My son, you have to eat Milan like an artichocke, leave by leave." Poland is an elective monarchy which always falls into disorder when its king dies. This is the time to benefit from that, and to win by virtue of our neutrality here a city, there a district, until it is swallowed in its entirety. Those lucky enough to bring that acquisition to its end will without doubt want to fortify Thorn, Elbing and Marienwerder as well as found smaller towns and places along the Weichsel, which shall thwart any attempts Russia makes against us. It is true that its regular troops needn't be feared, but its Kalmyks and Tartars are murderous and savage hordes which rampage through the lands and take entire peoples into captivity [...]

I hope that helps a bit! Political testaments are certainly a fascinating source, but like everything else they need to be read carefully and between the lines and they are always to be seen both as an attempt of a monarch to control his or her public image even after death as well as direct advice intended for their successors so that they might continue what the author had begun.