from Boston I guess you have to fly to Copenhagen... from there, Aarhus is 3 hours by train... Helsingborg is just in front of the Copenhagen on the Swedish side... I now Norwegian Airlines has a daily direct flight to NY pretty cheap (thats what I did last time)... there might be Icelanair flights Boston-Copnehagen via Iceland too (not sure)
There's also an airport in Billund, thats 1 hour from hour by bus... but dont think they have Transatlantic flights
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