Kursk Station, the Moscow terminal for trains to/from central Russia (Kursk and Nizhny Novgorod), eastern Ukraine (Donetsk and Kharkiv), and some Sapsan high-speed services from St. Petersburg is a little less than 10 km by road from the Cosmos Hotel.
By taxi
The drive to the Cosmos Hotel from the station will take 20-30 minutes in reasonable traffic, or more at peak times. Taxis should cost $30-40, or to save trouble you can book a transfer with driver to meet your train here.
By metro
From Kurskaya Metro Station, which is connected to the concourse of the mainline station, take the brown circle line two stops counterclockwise to Prospekt Mira, change there to the orange line and travel three stops north to VDNKh. The Cosmos Hotel is about five minutes' walk from the metro.