"I don't know" is used when you don't have the answer for the question.
"I have no idea" is a response to an suggestation.
A: Where is Mary?
B: I don't know (You don't know where Mary is)
A: Let's go shopping. Do you agree with me, B?
B: I have no idea.
A: And you, C?
C: I like to go movie better.
If sth's wrong, plz correct it. Thanks.
Sorry about my poor explaination. And now using Vietnamese.
"I don't know": Toi khong biet cau tra loi.
"I have no idea": Toi khong co y kien.
Student or Learner