What is the exact meaning of vicinity of Black hole or a disk? the same as inside?
From the Oxford English Dictionary:


  "vicinity" just means "the area near to or surrounding a place" 


so "in the vicinity of a black hole" just means "near to a black hole." 

Other dictionaries say "immediately next to" so in response to your comment about vagueness, treat vicinity as the immediate neighbourhood of the black hole. You will not find an exact meaning - it is used as it is in English. There is no specific distance measurement. You don't have a distance from radius which would stop being in the vicinity.