Kiev — A black-and-white photocopy of Vladimir Putin’s face hangs on a dartboard in the meeting room of an old Soviet sanatorium a few miles west of Kiev. The building now serves as a temporary home for several Crimean refugee families, and a couple of young men residing there hand me darts and encourage me to aim well at Putin’s face, which is already speckled with holes. Since Russia annexed Crimea, thousands of refugees have fled. Officials in Lviv region alone say they’re preparing for the influx of around 2,000 refugees. Meanwhile, in late March, Ukraine’s social-policy minister said...