How do I get from the hotel to the Tretyakov Gallery?

The most convenient option is certainly a taxi direct to the gallery, which can take over an hour and will cost at least $50. If you are ready to leave before 8am, you can use the hotel's minibus shuttle to get to Planernaya Metro Station, and from there take the purple line south eleven stops to Kitai-Gorod. Change there to the orange line and continue south one stop to Tretyakovskaya, which is around five minutes' walk from the gallery.