Swiss, United, Austrian, and Lufthansa have round-trip flights from Chicago (ORD) to Prague or Riga (PRG, RIX) for $522-$565 with a connection. Most flights are between October and March.
Lufthansa “Light Fares” allow for a carry-on bag (17.6-lbs @ 21.6 x 15.7 x 9 inches) and also a very small personal item such as a laptop bag (11.8 x 15.7 x 3.9 inches). The weight limit will probably be the limiting factor for those of you who wish to avoid bag fees. Prioritizing heavier items in your “personal item” may be a good way to lighten your carry-on bag. You can avoid seat selection fees by accepting the randomly assigned seat at the gate.
Click for more details and booking links Cheap Flights: Chicago to Prague or Riga $522-$565 r/t [October-March] – Swiss / Austrian / Lufthansa / United