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My mother wants to retire there. It's the only place in Russia that's warm enough for her.

yeah, climate here is rather warm. And Sochi is warm too btw.
But why have you chosen Russia? if it's not s secret;)

I've been looking to move back for years now, it's just a matter of where. I've narrowed it down to St. Petersburg (where I'm originally from) or Murmansk, since I have a friend who lives just across the Norwegian border in Alta. I like the cold, if you couldn't guess. My mother doesn't, and she wants to move because anywhere in America that has nice weather is either too expensive, too restrictive, or a war zone.

St. Petersburg and Murmansk are both in the north, and they are cold yeah. Southern cities are better for sure.
Now something strange is happening with climate and weather (just like with everything in the world...) but here the weather are warmer for sure. And Sochi is noce too, it has tropical climate, it's even warmer than Crimea (as a rule).