jeoneun naeil gajokgwa yeohaenghaeyo.

저 means “I” (humble/polite form). The particle -는 is a topic marker, so 저는 literally means “as for me….” In Korean, you often introduce the topic first. Using -는 instead of the subject marker -가 (저가) shifts the focus to what you’re going to say about yourself rather than emphasizing “I” as the new or unknown subject.

Time adverbs like 내일 (“tomorrow”) can drop the particle -에 when their meaning is clear.

• 내일 alone already means “(on) tomorrow.”
• Adding -에 (내일에) is not wrong, but omitting it is more natural and common in spoken Korean.

가족 means “family,” and -과 means “with” (literally “and,” but here used as a conjunction meaning “together with”). So 가족과 = “with (my) family.”
Alternatives:

• 가족하고 (casual)
• 가족이랑 (very casual)
  All three mean “with family,” but -과 is slightly more formal than -하고/이랑.

There are two common ways to say “travel”:

1. 여행하다 (“to travel,” noun+하다) → 여행해요 in polite present
2. 여행 가다 (“to go travel”) → 여행 가요
   Both are correct; 여행해요 focuses on the action of traveling itself, while 여행 가요 emphasizes “going to travel.” Native speakers use them interchangeably.

The -아요/어요 ending (here 해요) is the standard polite (deferential) style used in everyday conversation with people you don’t know well, coworkers, teachers, etc.

• If you want to be more formal: 여행합니다
• If you’re with close friends/family: 여행해 (informal)

Korean follows Subject–Object–Verb (SOV) word order. Even when you have adverbs or phrases for time/place, the main verb typically comes last. Here the breakdown is:

• Topic: 저는
• Time: 내일
• Companion: 가족과
• Verb: 여행해요

Yes. In Korean, if the subject/topic is clear from context, you can drop it. 내일 가족과 여행해요 still clearly means “I’m traveling with my family tomorrow” when it’s obvious you’re the speaker.

You insert the location before the verb with the particle -에:

• 저는 내일 가족과 부산에 여행해요.
  Literally: “As for me, tomorrow with my family to Busan I travel (politely).”