You can fly to Dublin, Ireland, for as little as $427 round-trip on several Star Alliance airlines.
http://www.secretflying.com/2016/05/mega-post-us-cities-dublin-ireland-427-roundtrip/
Winter travel, from a variety of U.S. cities, on Air Canada, Lufthansa or United.
While you may not want to spend a lot of winter days in Dublin, remember that it is the hub city for ultra-low-cost Ryanair. Ryanair flies to numerous European destinations, sometimes for just a few dollars per ticket plus miscellaneous add-on fees.