Tap Air Portugal has round-trip flights from New York (JFK) to Prague (PRG) for $369-$401 with a connection. Flights in May and October. Departures on Monday, Tuesday, Wednesday, Thursday, and Sunday. No Fridays or Saturdays. 7-day minimum stay required.
Carry on bag with a maximum weight of 17.6 lbs is allowed for free on TAP. You can avoid seat selection fees by accepting the randomly assigned seat at the gate. Upgrading to a higher fare class that includes a carry-on bag for $65 may be cheaper than booking the “Discount” fare with the added $95 carry-on bag fee.
TAP allows for free stopovers in Lisbon if you want to visit their hub-city before moving on to your destination.