American Airlines and Oneworld partners have round-trip flights from New York (JFK) to Copenhagen (CPH) starting at $332 with a connection. Flights October to May. Flight may operate as a Finnair code-share.
Note: New Years Eve is available if you can do a 10-day stay or longer.
Note: Fare allows for a free carry-on, but checked-bags will cost +$60 each-way. Upgrades into “Regular Economy” are available for about +$90 each-way.