There are 3 flights from all New York airports, USA to Russia, operated by 1 airlines. You can fly low cost from New York to 3 cities in Russia.
Kaliningrad
Moscow-Domodedovo
St. Petersburg
Fly on workdays: As many passengers prefer to fly on week-ends, week-end tickets sell first. If you don't book your trip well in advance (2-3 months beforehand) you may notice, for example, that Thursday flights are cheaper than Sunday flights. Some low cost carriers have special promotions on the flights during the week.