I've sailed in the Black Sea and been around most of the shore by land.
(which now includes Crimea) is fairly nightmarish bureaucratically, but Crimea is fascinating and could be worth the trouble to see. The worst part is you have to clear in and out every time you sail to another port; so maybe if you choose just one port it might not be so bad.
is gorgeous but also bureaucratically challenged. Abkhazia is one of the most beautiful spots on earth but this is a disputed territory -- use caution and get latest info before going.
Bulgaria, Romania -- you can get all the info from Noonsite.
has some charms (ancient cities like Trabzon).
It's a large area so you would want to pick one region if you only have two months. Maybe N Turkey, Georgia, and maybe Abkhazia (if that's feasible at the time you go).
Georgia is incredibly interesting and worth leaving the boat and going inland to explore, if you've never been there.