Fly from New York to Krakow for $696 round-trip, including all taxes, on Air Berlin.
This fare is part of Air Berlin's current fall/winter sale, good for travel from October 15 through March 31. As seen by the image below, we found seats departing JFK on October 17, and returning from Krakow on October 24.
Plenty of other European destinations to choose from, including Stockholm, Gothenburg, Oslo, and Warsaw. Flights connect via Dusseldorf or Berlin hubs.
All fares must be booked by July 31. Sale details at AirBerlin.com.