The absolute centre of a guitar is the strings - the rest is just support equipment.

After that, it becomes apparent that the neck is possibly a bigger influence on how the strings vibrate than the body is. There are a lot of strongly-held different opinions on this (which I'm sure are about to appear here), but I think it's fair to say that the neck material and construction, the neck-body joint, and the body material, are the major factors.

My own opinion is that the neck and fretboard materials are probably the most noticeable influences. I tend to select guitars with maple necks and rosewood fretboards. I prefer neck-through-body construction, but set-neck is acceptable, and bolt-on necks are just not good enough. I find that the body material is less of a contributor to the final sound of a solid-body electric guitar than the choice of strings, bridge type, and pickups.

That should stir up a few hornets! :D