
Ever since she was a tiny child, Sabriel has lived outside the walls of the Old Kingdom, away from the random power of Free Magic, and away from the Dead who won't stay dead. But now her father, the Mage Abhorsen, is missing, and to find him Sabriel must cross back into that world. Though her journey begins alone, she soon finds companions: Mogget, whose seemingly harmless feline form hides a powerful and perhaps malevolent spirit; and Touchstone, a young Charter Mage long imprisoned by magic, now free in body but still trapped by painful memories. With threats on all sides and only each other to trust, the three must travel deep into the Old Kingdom, toward a battle that will pit them against the true forces of life and death, and bring Sabriel face-to-face with her own hidden destiny. A tale of dark secrets, deep love and dangerous magic, Sabriel introduces Garth Nix as an exceptional new talent.
I read the first few HP, and thought they were dreadful, and thus never read the later ones, so maybe I'm not the person you want advice from, but here are some recommendations of novels/novelists in the same genre (fantasy novels, written for children, that hold up for adults):
Nearly anything by Dianna Wynne Jones, but I particularly enjoyed The Lives of Christopher Chant, Archer's Goon, and of course Howl's Moving Castle.
Susan Cooper's famous Dark is Rising series. Half the series is more normal-kid (starting with Greenwitch), half is more special-magic-kid (starting with The Dark is Rising).
Garth Nix's Old Kingdom, starting with Sabriel.
While China Mieville is very much not a children's author (really! don't buy a random mieville book for your young niece/nephew, really don't!), Un-Lun-Dun is an amazing book in this genre.