The hardback version, pictured below, actually has two Harry Potters on the front cover. The first is a close up of him looking out towards the reader. The second sees him flying on his broomstick - the Firebolt - clearly in the first task of the tri-wizard tournament. You can clearly see the golden egg he's trying to snatch from the grip of the dragon, although it doesn't appear to be a Hungarian Horntail. There is also a row of large plants running around the book to the back cover, probably a representation of third task.
The back cover has a picture of the house-elf Dobby, covering his mouth with his hand.
Also note that the author name says Joanne K. Rowling rather than the usual J.K. Rowling - something I imagine she approves of.