By "check it out", you mean "find out something's availability or something", and does it mean "I will go there"? The translation goes "I will go there", so I was confused.
M : I didn't see you at the art exhibit.
W:Oh, I decided not to go.
M:But you'd been talking about it for weeks.
W:I figured the museum would be crowded.
M:Well, you were right. It was packed.
W:I think I'll check it out sometime this week.
Q: Which is correct about the woman according to the conversation?
a. She will not attend the art exhibit
b. She delayed her visit to the museum.
c. She saw a crowd at the museum.
d. She will go to the museum this weekend.
The correct answer is B. she had planned to go at the weekend but decided it would be too crowded. Then she says she will go this week instead. She has delayed her visit. In this context, "check it out" does mean she will attend. She'll probably go there and see how crowded it is and then decide whether or not to go in.