Read the Harry Potter books yourself, if you haven't already. This may stir memories of similar books that you read during your own childhood.
Look for works by other children's fantasy authors ' some of Roald Dahl's work is very similar in style and tone to J.K. Rowling's Harry Potter books. Also check out the works of C.S. Lewis, Lloyd Alexander, J.R.R. Tolkien and E. Nesbit, among many others.
Search out other school stories ' many of these will be by British authors. Kipling's "Stalky and Co.," and some of Enid Blyton's work, may be a good place to start.
Find other classic children's adventure stories - "Treasure Island," "The Adventures of Huckleberry Finn" and some versions of "The Three Musketeers" may appeal to your adventure-loving child.
Ask a children's librarian for recommendations. He or she will almost certainly be able to point you in the direction of other well-written fantasy novels for children.
Look for works by less well-known authors. Robert C. O'Brien's "The Silver Crown" is an excellent, though little-known, "dark fantasy" novel for young readers, and there are many other good books out there, though you may have to hunt to find them.
Check out online Harry Potter discussion groups. Other kids or parents may be able to recommend books that they have enjoyed.