SAS and Tap Air Portugal have round-trip flights from New York/Newark (EWR/JFK) to Europe (see list in full blog post) for $274-$380 with a connection. Flights vary, depending on destination, with most between the months of January to May.
Note: Getting to some of these destinations may require a long connection.
Note: Carry on bag with a maximum weight of 18 lbs is allowed for free on SAS. You can avoid seat selection fees by accepting the randomly assigned seat at the gate.
Here’s a list of the destinations on sale.