British Airways, American Airlines, Finnair, Aer Lingus and various other airlines have round-trip flights from Austin (AUS) to Dublin or Inverness (DUB, INV) for $526-$571 with a connection. Flights November to March. Departures on Monday, Tuesday, Wednesday, and Sunday. 7-day minimum stay required. No Thanksgiving dates.
Inverness is cheaper, but has less availability.
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.