Harry Potter and the Methods of Rationality by Eliezer Yudkowsky and the related sequences.
I would say HPMoR is like Gödel Escher Bach, but slightly simpler and more approachable, and looks at stuff from a different angle. And Eliezer is an excellent writer, just like D. Hofstadter -- and his style is even more fun!
If you're on HN, then you'll enjoy this book immensely.
But, out of all that (which I had to go look up on my Goodreads), HPMOR is what came to mind, both an engaging story, thought provoking ideas, and a lot of pages to work with :).