There's no question about it: The Phantom Tollbooth is a work of children's literature – that's where you should look for it in the bookstore. The main character is a young boy who goes on an adventure and experiences magic, discovery, and friendship, all classic elements of children's literature. Of course the magic parts – the talking animals, Subtraction Soup, and orchestras that play colors instead of music – help The Phantom Tollbooth fit pretty nicely into the fantasy genre, too.
Don't stop there, though. The Phantom Tollbooth is also a quest. Check out this passage, where the Humbug explains pretty clearly that the characters are on a quest:
"Ah, the open road!" exclaimed the Humbug, breathing deeply, for he now seemed happily resigned to the trip. "The spirit of adventure, the lure of the unknown, the thrill of a gallant quest. How very grand indeed." Then, pleased with himself, he folded his arms, sat back, and left it at that. (9.2)
When the characters themselves know they're on a quest, we're pretty sure we can call the story one. In this case, Milo, Tock, and the Humbug are on a mission to rescue two princesses and restore the Kingdom of Wisdom to its former glory. It doesn't get much more classic quest than rescuing a princess, that's for sure.
The Phantom Tollbooth dabbles in other genres, too. Some might say it's a satire or parody, while Adam Gopnik says, "'The Phantom Tollbooth' is an old-fashioned moralizing allegory, with a symbolic point at every turn" (source). For more on this story as an allegory (and to find out what an allegory even is), head on over to our "Symbols, Imagery, Allegory" section. We bet you'll learn a lot.