Visiting Mother Russia this December 2013

Well, best thing is if you have some friends here who can show you around.

Moscow and St Pete's centres are full of touristic areas and restaurants.
Kremlin, Red square, Mosfilm street and a lot of other things (including tens of museums and parks) in Moscow.
Dvortsovaya square, Hermitage, a lot of places connected with Russian rock music and others in St Pete.

If you're thinking other cities, try to go to small cities around Moscow (like Sergiev Posad, for example - there's the biggest mens monastery in Russia there).

If you really want to go East, try Kazan and Yekaterinburg. Or, if you wanna go extreme, Novosibirsk. But in this case try not to freeze to death with your Southern skin Just kidding, get some real warm clothes, that might help.

I hope it helps mate; if you want some more explanation, let me know.