I've lived in Moscow for about 4 years (leaving soon but I have really liked it).
Most of what everyone else has said is accurate.
I think the restaurant scene is constantly changing (I think improving, at least incrementally). Moscow has lots of energy and some interesting youth culture (from my Canadian perspective at least) but it can be tricky to find if you don't speak Russian.
Get some georgian food (hatchapuri, kin kali etc), try some Uzbek food (PLOV!).
Check out the above place for borscht, varenickie etc. As the name implies it is Ukrainian Cuisine but I am fond of it.
There is another Russian restaurant I really like but the name eludes me at the moment. It is in the same complex as this korean place "Hite", converted factory space, there is an actual farm scene in a glassed in section of the restaurant. Anyone else know what I am talking about?
There are new burger/deli type places popping up selling exclusively Russian produce (sanctions) that might be interesting for you (Farsh and Lavash- I can't anglicize the second one well, they have two spaces one is kiddie corner to Christ the saviour).
Not the hippest choice but I like scernickie (cheese pancakes) at Coffiemania (chain of coffee shops around the city).
Tourist stuff is well documented elsewhere online. Bargain at the markets. Take the metro, it is beautiful and consider going for a wander down some of the old boulevards. Stay away from nightlife around arbat as it sucks and is full of weird expats. Have a drink on the roof top of the ritz carlton looking over Red square. Consider getting tickets to go the the Bolshoi. The old stage is prettier than the new but both put on amazing ballets/operas. You can take tours of the old stage but the # of people they let in is limited. There is no real system to getting into the tours you just have to show up and push your way in (if you google this there is info on their website about the times)
Clothing is pretty much a wash. The devaluation of the ruble has made many things more affordable but I have never seen anything that really knocked my socks off (price wise). The GUM is nice to wander around.
http://www.the-village.ru has info about stuff happening in Moscow but is only in Russia (get your google translate on)