Many of these are Github-specific; at work we use a graphical diff tool that shows the two files side by side, marking where changes have occurred. It does exactly what it sounds like you’re looking for.
Meld works great for that.
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KDiff3; it’s not perfect (Qt-based I think), but it does show the original and new versions side-by-side so you also get a visual indication of what’s changed. As puffnfresh mentioned, meld is also good.
We also have a custom viewer that’s based on our Clearcase install.
Since I used to work there, I should probably plug FogCreek’s Kiln which focused from the beginning on code review. By default I think it just shows the diff with some context, but you can ask to see the whole file.
As of recently, it even supports that git thing people use. :)