Taxis into the city centre from the Park Inn at Sheremetyevo Airport cost upwards of $60, and you will want to allow at least an hour to reach the Tretyakov Gallery, especially during morning peak times. Alternatively, you can take the Aeroexpress train to Belarus Railway Station, and then continue to the gallery by metro. Trains run from Sheremetyevo Airport Station (around 300m from the Park Inn) every half-hour, and standard single tickets cost just over $10. The journey takes 35 minutes.
Then, take the dark-green line from Belorusskaya Metro Station and travel south four stops to Novokuznetskaya, which is approximately seven minutes on foot from the Tretyakov Gallery.
Then, take the dark-green line from Belorusskaya Metro Station and travel south four stops to Novokuznetskaya, which is approximately seven minutes on foot from the Tretyakov Gallery.