British Airways, American Airlines, and Iberia have round-trip flights from Atlanta (ATL) to Gothenburg or Stockholm (GOT, ARN) for $483-$540 with a connection. Flights March, April, October, November, and December. No Friday departures. Holiday blackouts.
A Carry-on bag and also a personal item is allowed for free on American. You can avoid paying for seat selection by accepting the randomly assigned seat at the gate.