British Airways, American Airlines, and Finnair have round-trip flights from Austin (AUS) to Budapest (BUD) for $469-$482 with a connection. Flights December to February. Departures on Monday, Tuesday, Wednesday, Thursday, and Saturday.
American Airlines, British Airways, Finnair, Iberia and various other airlines have round-trip flights from Austin (AUS) to Dublin (DUB) for $352-$426 with a connection. Flights October to March. Extended weekends available.
COVID restrictions are still in place but this may be worthwhile for the dates later this year and next year.