The following summary is from Wikipedia:

This book tells the story of Claudia, a precocious 12-year-old girl who feels underappreciated by her parents. She decides to run away from home just long enough to show her family what they would be missing without her. Unfortunately, she doesn't enjoy hardship or discomfort, which makes traditional running away problematic. To solve this problem, Claudia decides to stay at the Metropolitan Museum of Art in New York City. She persuades her younger brother Jamie to accompany her: he's quiet, but most importantly, he has a secret stash of cash he's accumulated by cheating at card games with his best friend, Bruce.

Much of the early part of the novel details how Claudia and Jamie settle in at the museum: blending in with school groups on field trips during the day to get a free presentation, hiding in the restroom at closing time to stay there, and emerging at night to bathe in the fountain and sleep on antique beds. During their stay, they become fascinated with the newest exhibit: a beautiful statue of an angel, suspected to have been crafted by Michelangelo. Their dwindling resources of time and money are spent trying to uncover the secret of the statue, hidden somewhere in the voluminous and erratically organized files of the statue's previous owner, Mrs. Basil E. Frankweiler.