United and Star Alliance Airlines have low fares down to $496 round trip from Newark EWR to Krakow for travel in October and around $525 from New York LGA to Warsaw.
Ukraine Airlines will fly you New York JFK to Warsaw for $499 or Rome for $500 round trip. There are 8 other cities at $500 round trip from JFK including Amsterdam, Paris and Prague. Many of the Ukraine flights require an overnight in Kiev.
Newark EWR – Zurich ZRH (Swiss) – Krakow, Poland KRK (Swiss) – Munich MUC (Lufthansa) – Newark EWR (LH)
Air Canada/Swiss CheapoAir.com ticket
New York LGA – Montreal YUL – Paris CDG (Air Canada) – Warsaw WAW (LOT) – Zurich ZRH (Swiss) – Montreal YUL (Swiss) – New York LGA (AC)
$525.26 round trip Mon Nov 14 – Tue Nov 22
Ukraine Airlines New York JFK – Kiev, Ukraine KBP – Warsaw WAW – Kiev KBP – New York JFK
Ukraine Airlines New York JFK – Kiev, Ukraine KBP – Rome FCO – Kiev KBP – New York JFK
Air France is $555 round trip JFK-Rome on these same Thanksgiving week dates.