Kursk Station is the Moscow arrival point for trains to/from central Russia (Kursk and Nizhny Novgorod), eastern Ukraine (Donetsk and Kharkiv), and some Sapsan high-speed services from St. Petersburg. It is a little less than 20 km from the Katerina Park Hotel.
By taxi
The drive to the Katerina Park Hotel from the station will take around 30 minutes in reasonable traffic, or much 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
Take the metro from Kurskaya Metro Station and travel three stops clockwise on the brown circle line to Dobryninskaya. Change there to the gray line, and continue your journey south six stops to Prazhskaya, which is only five minutes' walk from the Katerina Park Hotel.