da-eum jue bakmulgwaneul dasi bangmunhal geoyeyo.

에 marks a point in time (or destination) and means at / on / in depending on context.

• 다음 주에 = next week (at some point next week)
  You can often omit 에 in casual speech when the meaning is still clear:
• 다음 주(에) 박물관을 다시 방문할 거예요.
  Keeping 에 is safer and more standard, especially for learners.

을/를 is the object particle. It marks the noun receiving the action of the verb.

• 박물관을 방문하다 = to visit a museum (museum = object being visited)
  Because 박물관 ends in a consonant (관), you use 을 (not 를).

-(으)ㄹ 거예요 is a common future form meaning will / going to (a plan or prediction).

• 방문해요 = present/habitual, or sometimes near-future depending on context
• 방문할 거예요 = clearly future: I will/am going to visit

1) Take the verb stem: 방문하-
2) Add -ㄹ 거예요 because the stem ends in a vowel (하):

• 방문하- + ㄹ 거예요 → 방문할 거예요
  If the stem ended in a consonant, you would usually add -을 거예요 instead.

거예요 is a contracted spoken form of 것이에요.

• -(으)ㄹ 거예요 is historically -(으)ㄹ 것이에요 (it is a thing that...) but functionally it just means future will/going to in modern Korean.
  거예요 is very common in conversation and polite speech.

다시 means again and usually appears before the verb or before the verb phrase.
Common natural placements:

• 다음 주에 박물관을 다시 방문할 거예요. (very natural)
• 다음 주에 다시 박물관을 방문할 거예요. (also natural; emphasizes again a bit earlier)
  Both work; the difference is mostly subtle emphasis and rhythm.

Korean often omits the subject when it’s understood from context.
So this sentence can mean I will, we will, they will, etc., depending on the conversation.
If you want to include it:

• 저는 다음 주에 박물관을 다시 방문할 거예요. (I...)
• 우리는 다음 주에 박물관을 다시 방문할 거예요. (We...)

방문하다 means to visit and sounds a bit more formal or “written/official” than 가다.
Very common alternatives:

• 다음 주에 박물관에 다시 갈 거예요. = I’ll go to the museum again (more casual)
• 다음 주에 박물관을 다시 방문할 거예요. = I’ll visit the museum again (slightly more formal)
  Both are correct; choose based on tone.

Yes—because the verb changes what role the noun plays.

• With 방문하다 (visit), the place is treated like the direct object: 박물관을 방문하다
• With 가다 (go), the place is a destination, so you use 에: 박물관에 가다
  So the particle is tied to the verb’s typical pattern.

-거예요 is polite informal (the 요 style), suitable for most everyday situations.

• More casual (to friends): 다음 주에 박물관 다시 방문할 거야.
• More formal (to customers/official settings): 다음 주에 박물관을 다시 방문할 것입니다. / 방문하겠습니다.
  Choice depends on the relationship and context.

A natural pronunciation (rough guide) is:

• 다음 주에 → sounds like 다음 주에 (smooth, quick)
• 박물관을 → often sounds like 방물과늘 (common sound change: ㄱ + ㅁ can sound like ㅇ + ㅁ)
• 방문할 거예요 → 방문할 꺼예요 (the ㄱ in 거 is commonly tense in speech)
  So you may hear something close to: 다음 주에 방물과늘 다시 방문할 꺼예요.