Icelandair has round-trip flights from Newark/New York (EWR/JFK) to Berlin, Bergen Norway, Manchester, or Munich (BER, BGO, MAN, MUC) for $458-$480 with a connection. Flights February to May. Extended weekends available.
Some small OTAs on Skyscanner and Kayak have this for cheaper than the airline. If you plan on booking there, beware of any site that charges a fee to cancel a ticket within the 24-hour “free” period. Use unknown booking sites at your own risk.
A Carry on bag (20-lbs @ 21.6 x 15.7 x 7.8 inches) and a personal item (15.7 x 11.8 x 5.9 inches) is allowed for free on Icelandair. You can avoid seat selection fees by accepting the randomly assigned seat at the gate.
Icelandair offers free stopovers, which good if you want spend a few nights in Reykjavik. More details are on their website (link).
Click for more details and booking links Cheap Flights: Newark/New York to Berlin, Bergen Norway, Manchester, or Munich $423-$495 r/t [February-May] – Icelandair