Bitterblue by Kristin Cashore.
She's kept busy signing sheaves of paper, and seldom has time to leave her offices. One night, out of pure frustration, she "borrows" a cape from one of her servants and goes out into her city. She chances on a pub with a storyteller who happens to be telling about how her father, Leck, had come to Monsea when he was a boy. She also catches a young man, about her own age, in the act of picking a pocket, and follows him when he leaves. However, she's not quick enough to see where he went, and heads home.
Having enjoyed being her own spy, she knows that sitting at her desk and signing piles of papers is not the way to run her kingdom, though she knows she cannot tell her advisors this. She asks the Royal Librarian (!) to find her a map of the city, and goes out again the following night. It eventually turns into a routine for her.
The jacket-flap of the book indicates that it's not necessary to have read Graceling to understand Bitterblue, it is certainly helpful, especially understanding the political complexities of what is called The Known World. It also helps in understanding what Queen Bitterblue is up against.
Cashore has created an amazing World, with several different kingdoms, each with its own history and customs. She has even included within the story, a sort of primer to another language. Appendices contain maps of Bitterblue's rooms, her castle and The Known World as well as a Who's Who of The World As We Know It (basically a Cast of Characters) recorded by the wonderful Royal Librarian of Monsea.
FTC Full Disclosure : I borrowed this book from my local library.