From memory, there is no US military base on the Black Sea. The NATO bases in/near Izmir and Incirlik are decidedly Med/Mid East in orientation. Near the Middle East I understand. Location, location, location.
FWIW the 8 were found guilty on some charges (with suspended sentences) and they moved to Athens. If some of you thought the move have to do with a possible Turkish attempt to kidnap them, I am not sure what to say.