Vilnius Railway Station is located at the Old Town, at Geležinkelio st 16. Working hours are 0-24, so you can walk there whenever you need.
Distance from the Vilnius Airport to Vilnius Railway Station is about 5 km, the journey takes up to 7 minutes. Trains run approximately every 30 minutes. The schedule can be found at www.traukiniobilietas.lt . Tickets can be purchased online, on the train or at Vilnius Railway Station.