Final answer:
The correct answer is 'there'. So, the correct answer is option 1.
Step-by-step explanation:
The correct answer is 1) there.
'There' indicates place and is used to refer to a location. In the given question, 'Who is going to visit the Palmer Museum of Art?', 'there' is used to ask who is going to go to the museum. 'Their' is a possessive pronoun used to show ownership, and 'they're' is a contraction of 'they are'.
For example, if someone asks 'Who is going to the party?', you could answer 'They're going to the party' to indicate that a group of people is going.
So, the correct answer is option 1.