If you go to Russian run hotels they tend to be cheaper, but not as well run or as nice. But you get what you paid for.
The best hotel in Moscow was the hotel Rossiya, which was actually in Red Square and had views of Kremlin, St Basils etc. However, I think that it has since closed. I would recommend doing some research on this hotel. If it is still there, I highly recommend this hotel, as it has the best location. Whilst trying to submit this, I think that I have found that the hotel Rossiya is now closed.
There is an SAS Raddisson near Red Square, but is more expensive.
I recommend using Intourist website for hotel suggestions
http://www.intourist.co.uk/intourist/itmainsc. php the website seems to be very slow (get used to it!!) when trying to find their hotel suggestions, but they are on there.
Dealing with Russia ie visa's, hotels, tourist boards etc is like trying to push water uphill with a sieve - ie difficult!! I spent the best part of a month trying to get a trip to Russia sorted.