"stirring in the air" is an expression that can be applied to many things. so "war" is "stirring in the air" rebellion could be "stirring in the air" "the hint of change" could be "stirring in the air" "the end of a long slumber" could be "stirring in the air". "stirring in the air" means that a thing can be detected and the signs of it are visible, sometimes those signs are vague as in the case in this sentence - "something" is stirring, but what ? I think that "great day" here is referring to what the writer could achieve that day. He could have a "great day" writing a new novel as he was inspired or he could have a "bad day" where he is unable to write, then he would be suffering from "writer's cramp" - an inability to write.

'Something siring in the air' means something happening or going to happen that you can feel in the air. It is a subtle feeling . The writer is afraid that he will miss something happening outside if he stays inside. "great day" could be the writer's friend's own words.