As far as I remember this hotel was not bad. It is not in the centre, but close to the metro, which brings you directly to the red square in 20 min.

Booking.com : VashOtel - Voskhod Hotel , Moscow, Russia - 41 Guest reviews . Book your hotel now!

And this might suit you too. Quiet city cenre. But you'll have to walk 20 min to Red square.
Booking.com : Арбат Хаус Отель , Москва,


And another one. My friends parents were happy to live in it.
Booking.com : Отель Гостиница Кадашевская , Москва,

And this one. Cheap. But not very close to centre. I've been there just once and just in sport club. Seemed clean, but a bit shabby place.
Отель Гостиница Измайлово Бета - Booking.com : Москва,