Learn Hardcore Korean: gonghangeseo hotelkkaji taeksiro gayo. - I take a taxi from the airport to the hotel.

The particle 에서 marks the starting point of an action in space. Here, it tells us “from the airport.” Without 에서, it would just be a noun without indicating origin.

What does 호텔까지 mean and why use 까지?

The particle 까지 means “up to” or “until.” It marks the destination or endpoint. So 호텔까지 means “to the hotel.” Combining 공항에서 and 호텔까지 literally gives “from the airport to the hotel.”

Why is 택시로 used instead of 택시 or 택시에?

The particle 로 indicates means or method (“by taxi”).

택시 alone is just the noun.
택시에 would use the locative/dative 에, which is not correct for “by means of.”
택시로 specifically means “using a taxi.”

Could I say 택시를 타고 가요 instead of 택시로 가요?

Yes. 택시를 타고 가요 literally means “ride a taxi and go,” and it’s a natural alternative.

택시로 가요 is shorter and equally common.
Both convey the same idea of going by taxi.

What level of politeness is 가요?

가요 is in the polite informal style (often called “-요 form”). It’s appropriate for everyday conversations with people you don’t know well or who are similar in age/status.

If you want to be more formal, you could say 갑니다.
If you’re talking to close friends or younger people, you might use 가 (plain).

Why is the verb 가요 (to go) used instead of 오다 (to come)?

Whether you use 가다 or 오다 depends on the speaker’s perspective:

가다 (“to go”) is used when you’re moving away from your current location toward another place (airport → hotel).
오다 (“to come”) is used when you’re moving toward the speaker’s current location.
Here, you’re not at the hotel yet, so you use 가요.

Can I switch 공항에서 and 호텔까지 around?

No, because word order for origin and destination follows from–to logic:

공항에서 (from airport) 호텔까지 (to hotel).
Switching them would break that logical order and sound incorrect.

Could I omit the particles and just say 공항 호텔 택시 가요?

In very casual speech you might drop particles, but it becomes ambiguous and ungrammatical in standard Korean. It’s best to keep 에서, 까지, and 로 to clearly show origin, destination, and means.