American Airlines, Finnair, Iberia, British Airways and various other airlines have round-trip flights from Dallas (DFW) to Berlin, Nice, or Naples (BER, NCE, NAP) for $496-$605 with a connection. Berlin flights December to March. Nice flights October-May + August. Naples flights November + January-May. 7-day minimum stay required. No Christmas dates available.
Berlin is the most expensive destination in this group with flights between $581-$605. Other destinations are less than $540.
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.