Actually one thing a Nolan Superman movie could do is bring back the more grounded and down-to-earth Superman of the early comics-- before he became this all powerful, godlike being with magical superpowers.
Instead he would just be an alien with super tough skin whose muscles give him a huge advantage in Earth's lighter gravity. He might be able to leap great distances, but there'd be none of this flying and hovering in the air. And much like Batman, he uses those powers to become a crusader for justice; instead of fighting fanciful supervillains he uses his reporter's skills to hunt down and stop real criminals. And of course like any alien would, he'd have to deal with constant fear and suspicion from the people of Earth.
Frankly, I think the original version of the character lends itself really WELL to a Nolan-style movie. I'm not sure it's the kind of Superman most people would want to see though.