There are many first rate hotels in Moscow. I stayed at Metropol, actually for the second time. I stayed there a few years earlier although I had not recalled that when booking this trip. It was just one of the options offered by Incredible Adventures.
Very “old school” Europe including WWII damage to the building, but first rate in terms of accommodations and literally 100 yards or so from Red Square and all the surrounding things to see. For example the Bolshoy Theater is directly across the street.