Well, I'm not on the EDF thread starter list, so I guess I don't count [img]/images/graemlins/wink.gif[/img]. Either way, feel free to drop me a PM if you have more questions, or want to do drinks when you get here. If I'm home of course, I don't usually plan that far ahead.
As far as safety goes.. I'd say it is fairly similar to any big city, common sense gets you a long way. Specifically for Moscow/Russia: the militsia (police) is notorious for being corrupt. I have not had any negative experiences though - see to it that your documents are in order, and you should be fine. In the year and a half I've been here they asked for papers twice, so probably you won't even have to deal with them. Of course, don't draw negative attention to yourself, yada yada.
I could go on and on, but there is an excellent thread on the subject
here (Moscow expat forums).
If you don't have transport from the airport, know that less than three bucks will get you to the center of the city. That is, if you feel adventurous and take public transport, which is fairly decent but might be tough to figure out if you don't at least read Cyrillic. If you must take a taxi, don't get ripped off. My place is twice as far as the center, and last winter I paid 1200 rubles (under 50 bucks). So don't let some shady [censored] take you to your hotel for a hundred. Oh and don't change too much cash at the airport or your hotel if you can help it, booths on the street generally offer the best value. More info in the link.
The above paragraph assumes you arrive at Sheremetyevo (unfortunately most likely). The other airports have trains to the center, which are pretty much zero hassle. Some airport personnel ought to speak at least some English, they can tell you what to do.
As for must sees, I'm the world's worst tourist - my favorite part of sightseeing trips with the girlfriend is having a beer and a nice steak afterward. I dunno, look at Lonely Planet or something...
EDIT: if you're interested, there's a pretty decent live poker scene as well. My favorite place unfortunately kind of dried up as far as 5/10 NL/PL (they play HE, Omaha and dealer's choice games) and up, but there are other options. The names that come to mind are Asia, Orlyonok and Korona (fav place, just got back from a 5/5 game but with 5k stacks). The Shangri-La supposedly accepts players that are pretty much barred in all other places, but I know this only from word of mouth - went there once, they kicked me out for not being 21, then later heard the rumors and didn't go back when I was.
EDIT2: if you're looking for other entertainment, I recommend the Sandwich Lodge. Haven't been there in over a year, but a lap dance w/touching was RUR 100 or $4 a song. Again, use common sense here, don't show up with a CC/big wad of cash and don't order something unless you know in advance what it costs.