At the end of the book, Oskar finally finds the lock the key goes to, his Dad's secret diary is revealed, and Oskar's life changes forever.
Okay, no. Oskar may have wanted to find something like that (we're not sure what he expected to find) but he ends up finding out that the key goes to a safe-deposit box belonging to William Black's dead father. Oskar doesn't even go with William to open the box. It has nothing to do with him, and he doesn't care. While this journey may have changed William's life (he'd been madly searching for the key, too) Oskar's left with no answers.
Because of this disappointment, Oskar still has to invent closure, creating a fantasy world in which he and his father are safe. The books final pages are a flip book (honestly, you can flip them) of photos of a man falling to his death from the World Trade Center, a man that Oskar thinks might even be his father. Oskar reverses the photos so that when you flip them, the man falls up. He creates a fable, like the Sixth Borough, in which his Dad is still alive. His final words at the end of the book are "We would have been safe" (17.162).
The hard truth is that no matter where the key led Oskar, it wouldn't have provided him with any closure about his Dad's death. Dad died tragically, and there's no changing that. Oskar's going to have find closure from within. No scavenger hunt will lead him to it.