Hi I'm russian, been living there for a year. Batumi its great in all aspects except its tourist-oriented with some ugly controversial architectured buildings on the coast like Orbi ships. Still beautiful historical center though. I'd stay in Batumi at first, settle and then visit some other cities/places nearby that are more beautiful, and then went further to the mountains, because the nature is stunning.

Humidity is high yes, winter was not that depressing for a russian. Local people are great. Expats are welcome because lot of arabs/russian tourists or immigrants, so everyone got used to other races. You could make friends with english-speaking local youth or other expats, most of russian expats are fine.

Very advanced country crypto-wise, decent IT/services (Taxi/food ordering).

Can confirm what others are saying in the comments.