Sochi is a pretty big city/area, and that is right there.
The ski area is Rosa Khutor, which is inland a bit from the city area
You are correct with the place was pretty much built from scratch. Russia dumped a lot of money into it. 40 rope way systems from Doppelmayr including one of the longest and fasted gondolas in the world. SMI put in all the snowmaking with 100+ fans and 12,000 gmp system. Insane. Not to mention all the hotel and road infrastructure. Already over $40b in costs and that is just still going up.
Not to mention the weather is wack in that region. One system will come in with 5' of snow, next systemwill be 2" of rain. The snow storage they have in place is one of kind. That has never been done before and is quite impressive.
Also the main venue for bumps/arias/pipe is awesome. Such a good layout.
I could go on and on, but all I can say is I am very curious to see how it all plays out once they games start.