i was just in moscow a couple weeks ago and loved it! i found it VERY hard to get around and spent a lot of time kind of lost (not being able to "follow the crowds" was part of that problem, too). once you figure it out it's a great city and the metro is amazing.
i went on 3 tours with
http://www.capitaltours.ru/. i hope you get natalia if you do it!! i HIGHLY recommend the metro tour with her (only offered on sundays and after riding on a weekday i can completely understand why, it's a mad house of people plus with low numbers sunday mornings it's easy to take in the whole platform). i also did the red square tour and the kremlin tour with them. natalia is great if you get her otherwise some of that you can do on your own, unless you want a lot of history lessons. might be good though if you're there at high time you probably get in faster with a guide. also the kremlin tour has to be booked in advanced because they have to prepurchase tix and register you and there's a minimum number required. their office is right by GUM (mall adjacent to red square) so is easy to find. i spent around 100 USD for all 3 tours, which is very reasonable considering the cost of the rest of the city and relative to other tours in other cities/countries. worth more than i paid!
in general, the food there was nothing to write home about. we went to cafe pushkin. very expensive and i can't say i really enjoyed anything there. also went to this georgian place genatsvale--that food was good, but we were with georgians so i never even set eyes on the menu. find a "canteen" restaurant like the one on the 3rd floor north end of the GUM for a quick and super cheap and more homestyle/authentic meal (went to a similar place with the guide when i had a break in between tours).
the grocery store inside GUM has some neat stuff to look at and you can grab a bit there. also the grocery store Eliseevskiy on Tverskaya
http://eliseevskiy.ru/e_about.htm is worth stopping in to for a look around if you're in the area.
lenin's tomb was interesting. not amazing but a must do i think since it's pretty unusual. no camera's or cell phones so make sure you first check your junk (40 rubles) at a window on the corner of the big brick building (history museum i believe) and then go thru security. i was lucky as there were not really lines when the weather was 5F so it only took me about 10 minutes in all but i imagine it's much busier other times (as indicated by the way they made me go through a roped off queue 3 times the distance to the front door with no one ahead of me.
i can't speak to a lot of other stuff there is to do there because it was so cold and i wasted a lot of time being lost, not knowing how to get a ticket, cross the street, etc!! but it's a great city and i'd definitely go back.
my #1 piece of advice is to definitely get a guide somehow to help you navigate otherwise you'll never get as much done as you'd like to there.
and make sure you apply early for your visa. i was borderline on my receiving date and they suggested i pay an extra $100 to rush it (and i actually got it way faster than the slow suggestion...but safe then sorry right?)
sounds like an amazing trip!! enjoy!