The fastest way to reach the Kremlin from the Holiday Inn Simonovsky Hotel is to take the metro from Proletarksya Station (400 m from the entrance of the hotel) on the purple line three stops north to Kuznetskiy Most and then change to the red line and travel two stops west to Biblioteka im. Lenina, which can be exited right next to the main visitor entrance of the Kremlin.
Back to Holiday Inn Simonovsky Hotel