I think Conway and Guy's "The Book of Numbers" might be a better source. It's more focused on infinities as different types of number, and certainly at a more suitable level. ONAG is quite a technical book; children don't really need to know that the surreals are the universally embedding real-closed field.

Another book I really liked that talks about infinity is "A Certain Ambiguity", by Gaurav Suri and Hartosh Singh Bal.