The Holiday Inn Simonovsky is just over five minutes' walk from Proletarskaya Metro Station on the purple line and Krestyanskaya Zastava on the light-green line. From there it is just two stops to Kitai-Gorod, and five stops to the Kremlin, Red Square and the Bolshoi Theater. To reach the station, turn left out of the hotel, take the second right onto 3-y Krutitiskiy Pereulok and walk down the street till you see the metro on the right side.
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