The damage is very obvious. He revealed a bunch of mediums that the NSA had the capability to monitor. Any sophisticated actor that wants to avoid US intelligence is now avoiding those mediums.
My point is that he didn't have to flee. Instead he fled into the arms of those who stand to gain the most from his knowledge of our intelligence capabilities. Putin is not giving him asylum for free. I'm sure he's getting something out of it, if just the ability to use Snowden as as a propaganda piece and negotiating chip. It'd probably be hard to make a treason charge legally stick, but I believe it is what he is morally guilty of. There are plenty of things that he is plainly guilty of that carry equivalently harsh sentences.
You're right, he had nowhere else to flee but the enemies of the United States. But that doesn't change the fact that he fled, nor where he fled to. He did not have to flee. And yes, I think he's a coward for it.