In addition to a tour of Red Square, make sure that you also set aside time to go through the Armoury Museum which is located inside the Kremlin. This is where you can see all of the ancient religious and political artifacts from Russia, crown jewels and throne, Faberge eggs, etc. Well worth the visit.
When I went, my company hired a local tour guide for me. I'm sure that there are plenty of English speaking guides that you can find if you ask around. One of the key benefits to such a tour guide is that they should know how to avoid the lines to get in to the Kremlin, Armoury, etc. I'm sure I paid extra for the "Express" ticket but, after having seen the line to get in, it was well worth it.
While it will indeed be brutally cold in Moscow, nothing beats the experience of standing in the middle of Red Square during a snow storm, with ice skaters on an outdoor rink in front of GUM, with St. Peter's onion shaped spires covered in snow, etc.
Definitely hit Arbat Street if you get a chance. Plenty of places selling souvenirs (I found Aggie nesting dolls as well), old military patches and pins, and such.
The Metro, especially during Winter time, is your friend. Make sure that you have a copy of the subway map and that you can at least match the Russian Cyrillic on the map with the signs on the stations. The lines each have a different color and shouldn't be too hard to figure out which is which. Just make sure that you are heading the proper direction on the line and count the number of stops until your destination. Worse comes to worse, get off, and get back on a train heading the other direction. The ticket you bought gives you unlimited admission throughout the Metro as long as you don't go out the surface exit.
Buying tickets for Metro can be a bit intimidating as the ticket seller always seems to be a gruff old woman who yells at you if you aren't fast enough. But all you have to do is hold up a single finger as you lay your cash down and she should understand that you want a single ride ticket.
Watch out for the cars when you are crossing streets or walking on the sidewalk. They won't hesitate to run you over and, if it has been snowing or icy which it will be, they seem to take special pleasure in hitting the puddles and trying to drench you as they go by.
Also be careful in the evening or in isolated areas. There are underground passages at most major intersections so that you don't have to fight traffic to get across. Again, during winter time, these are nice but later at night, they are probably best avoided because you can find a wide variety of low lifes down there once the working crowd clears out.
If you are out late (or up early) and get a little homesick, visit Starlite Diner. It is an American Diner, maltshop type of place that servers burgers, shakes, fries, etc. Can't tell you exactly where it is except that it is in a small park near the center of town and across the street from the Peking Hotel. Besides the taste of home, it is always fun watching the other groups who show up there, typically after a night of boozing at the nightclubs.
Can't say much about the restaurants. Goodman's is a nice (and expensive steak house) but I don't really go to Moscow for steaks. I have been to several smaller restaurants and had some great meals. Don't leave without having at least one meal of Stroganoff. And if you find yourself hungry while walking around, you can always find a "Krap Dog" hot dog stand for a quick snack. They have a few different types of buns and franks to choose from but you can just point at which you want and you will be ok.
