Both sentences are grammatically correct, but they convey slightly different meanings: "They are talking in the museum." - This sentence suggests that the people in question are having a conversation while inside the museum. It implies that they are somewhere within the museum building, such as in one of the exhibition rooms or galleries. "They are talking at the museum." - This sentence implies that the people are having a conversation in the general vicinity or vicinity of the museum but not necessarily inside the building. They could be outside the museum, in the parking lot, near the entrance, or in some other area that is close to the museum but not necessarily within it. The choice between "in" and "at" depends on the specific context and what you want to emphasize about the location of the conversation.

"In" and "at" are both correct. In fact, I can think of few prepositions that would be incorrect. They could be talking "under the museum", "above the museum", "beside the museum", "for the museum", "behind the museum", and so forth.. So don't worry about whether the sentences are right or wrong. Using a dictionary, think instead about what each preposition means. Look up a list of English prepositions and try them one by one in your sentence. Ask yourself what the sentence means.