Trip to Crimea and Southern Russia

Hello everyone!
Next summer I want to travel to Crimea and Southern Russia, the trip should take about 3 weeks, I am not on a very limited budget, but it shouldn´t be very expensive either.

I have considered to visit most parts of Crimea (Simferopol, Sevastopol, Yalta,...).
What are the places which you "have" to see? What should I avoid?

I am very insecure about what to see in Southern Russia.
When I come from Crimea, my first stop could be Krasnodar. Does anyone have experiences with it?
Then I thought about getting to Sochi. Is it worth seeing? How many days should I plan for it? Where should I stay (Sochi is so long, I can´t really find a "city centre")? Will there still be many construction work going on for the Olympics?
I am also interested in Elista and maybe Derbent, has anyone been to these cities?

What is the best way to see those four places? Or is one of them not worth visiting? What is the best way to get aroung? Train, bus, airplane?

Thank you in advance!