I have stayed in many: some more expensive and some more reasonably priced. Now however that the RUB is down, you will be able to get very decent details.

If you want 5* ones, my favourite is the Swissotel. It is not the closest one to Red Square but you can walk there along the river in roughly 15mins if you dont get lost .

The Metropol is also pretty decent hotel-wise, and in terms of location, its among the best. The Hotel National is also very close to Red Square, so a good option if you dont mind paying a bit more.

If you want something cheaper (the above three are 5*), I suggest you look for something along Tverskaya. I personally like the area near Beloruskaya, a few nice bars around and very well communicated. You can also walk pretty much anywhere from there although early March might be cold.