Fly from New York to Vilnius (that's Lithuania, in case you're wondering) for $381 round-trip, including all taxes on AeroSvit Airlines. Availability is scarce, but we managed to find seats for early April, via Vayama, as seen below. Travel Tuesdays and Fridays.
Available for the same price, dates for Kiev, Ukraine are a tad easier to come by. Travel in mid-April on Tuesdays, Thursdays, Fridays, and Sundays.