Living in a big city

Living in a big city is equal to a busy but fulfilling life. Every time I arrive at the subway station, I marvel at the number of people who are trying their best to survive in the big city. They smile, cry, hug  and say goodbye here. Those who leave their families behind have a dream that one day they can have a home here. But in most cases, they will be exiled from the big city due to the high  cost of housing  and high living costs. Maybe years from now, one day, they will come back to the city they had been to and  think"I have devoted all my youth here"

exiled - is not the correct word.  "exiled" means that they have been removed (often by force).
You could say something like, "they won't be able to live here" or "the cost of living is too prohibitive for them"
or "they can't afford to stay here due to the high cost of living." 

"high cost of living" includes housing, so you don't have to say "high cost of housing" and "high living costs"
high cost of housing -- any type of housing (from sharing a room, to renting an apartment to buying a house)
If you are talking about purchasing a house, you can say" due to the (high/exhorbitant) price of houses"