Via The Points Guy, you can fly round-trip from several US cities to Copenhagen, Helsinki, Oslo, and Stockholm, starting at just $347 in coach!
It looks like this fare is valid primarily for travel between January and March 2017, though there are also dates available in April and May 2017. I found flights from Boston to Copenhagen for $347 on April 2, 2017, and returning April 10, 2017.
Here are the details. And how to search for deals from your city!