I loved Goldblatt's book, "Lectures on the Hyperreals".
For a more sophisticated treatment, don't overlook "Nonstandard Analysis: Theory and Applications", edited by Henson (first chapter available there) and others. It seems at first blush like a collection of articles, and it is, but they are introductions to various uses of NSA and came across quite well to me. That is, the article on topology assumes that you know some standard topology, and the article on probability assumes that you know some measure theory and probability, and so on.