Why did the Russians choose Sochi as the location for the Winter Olympics? Judging by two main criteria, their choice is rather poor:

 

Climate

Russia is known for its harsh winters. They have never hosted a winter olympics ever, so you'd assume they have all of Russia to choose from. And yet they choose a sub-tropical humid location, which has a warmer climate than any previous winter olympics, ever. It is also one of the most southern locations in all of Russia.

 

Political

Sochi's Olympic park is located merely 4-5 km from the border with Georgia (Google maps), with whom the Russians have fought a short war as recently as 2008. It is also located merely a couple hundred kilometers from another separatist/rebel/fundamentalist-islam area (Chechnya) where groups seem to seek independence from Russia for several reasons. In fact, the whole Caucasus is a hotbed for struggles.

 

So, is this just a trick to extend Russian influence into the Caucasus? Or is there another reason? Any thoughts?

You need mountains for the alpine skiing, so that rules out areas not near mountains, and you need a transportation hub. Also the choice was made in 2007, so events in 2008 had no effect on the decision.