The easiest way to get to the main collections of the Tretyakov Gallery (the "Old Tretyakov") on Lavrushinskiy Pereulok is to take the metro from Paveletskaya Metro Station (less than ten minutes' walk from the Swissotel) and travel north one stop on the dark-green line to Novokuznetskaya. Exit the metro via the connected Tretyakovskaya Station, and you emerge above ground about five minutes' walk from the Tretyakov, with signposts from the metro to guide your way.
Back to Swissotel Krasnye Holmy