He chose to be out of the country when the story dropped. It was at least partially his decision to fly through Russia. He could have stayed in the US, faced the charges against him, argue his case in court, and tried to seek justice that way countless civil disobedients did before him.
Snowden ended up in Russia by accident. He was flying from Hong Kong to Ecuador, and his flight happened to be laid over in Moscow when the US government cancelled his passport. He spent a month and a half living in the airport before he gave up trying to leave Russia and asked for asylum.
If he could have gone anywhere else it seems likely he would have done so.