Kursk Station is the Moscow terminal for trains from central Russia (Kursk and Nizhny Novgorod), eastern Ukraine (Donetsk and Kharkiv), and some Sapsan high-speed trains from St. Petersburg. The Sputnik Hotel is just 10 km from the station.
By taxi
It should take around 30 minutes to reach the hotel by car, although the trip can be much longer at peak times. If you are willing to negotiate with a driver on arrival, taxis should cost no more than $40. If you prefer, you can book a transfer with a driver to meet your train here.
By metro
If you prefer to use public transport, take the metro from Kurskaya Metro Station (attached to the mainline station) on the brown circle line and go four stops clockwise. Then, change to the orange line and from Oktyabrskaya go south two stops to Leninsky Prospekt, which is only 10 minutes; walk from the Sputnik Hotel.
