Sorry but I don't know Moscow well enough to recommend a good place.
But I would like to mention that it'll be extremely cold outside, so I would suggest looking for a place inside that'll have a view.
One of the hotels or restaurants in some of the high buildings.
It doesn't really have to be that close to the Red Square if you are high up (and facing the right direction).
I saw firework (celebrating Moscows birthday) in September from my room on the 17. floor of the Hilton Leningradskaya.
There was firework in different locations so I have no idea which I saw.