Pick through the stuff by Dover publishing. They have some very intense math books, but there are definitely some books about math for "lay people". Many of them can be had cheaply, and there are usually plenty of reviews on amazon to figure out what is both interesting and accessible.
I really like the Dover book Mathematics for the Nonmathematician by Morris Kline. It adds historical perspective, makes you think, and teaches basic and understandable proofs.
