*What does "I want you around" mean?
The simple answer is that it means: I want you to be near at hand, in the vicinity.
"Please stay in the office today, I want you around when the new guy starts, he'll need help".
or conversely: "My girl friend is visiting this afternoon and I need some privacy, I don't want you around".
But the meaning can change with context.
For example: "I want you around there immediately" can mean "I want you to go around there immediately".
* I want to know if this statement is correct.
"I'm always tripping over the same rock all the time."
As it stands, the repetition would sound a little unnatural to a native speaker.
These are better:
"I'm always tripping over the same rock".
"I keep tripping over the same rock all the time".
In conversation, possibly: "I'm always tripping over the same rock, all the time!"
The repetition emphasizes that this just keeps on happening.
not a teacher
Student or Learner