I liked "Godels Theorem Simplified". Although it looks like it is now a lot more expensive than it used to be. Maybe get it through and interlibrary loan.

https://www.amazon.com/Godels-Theorem-Simplified-Harry-Gensl...

I liked _Godel's Theorem Simplified_

http://www.amazon.com/Godels-Theorem-Simplified-Harry-Gensle...

I always liked "Godels Theorem Simplified". It doesn't rely on heavy technical prerequisites in mathematics or CS. It is pretty much as advertised, a simplification of Godel's original proof. Godel used a more complicated encoding scheme using prime numbers, which Gensler replaces with a simpler encoding scheme. He walks you through various less powerful formal systems, before you get to one complicated enough to have incompleteness issues. There is also discussion about the philosophical ramifications of Godel's theroems.

http://www.amazon.com/Godels-Theorem-Simplified-Harry-Gensle...

"Godel, Escher, Bach" is another interesting read, but that volume does have a lot of extraneous fluff.