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Yes, it is very bad in Spring.
I'd like to escape from Seoul next week

fly to Jeju
but I guess the yellow dust gets there, too

better yet, you should check out Philippines @slowwalkernim
specially this time of the year - cheap flights
go to the beach
there we don't have yellow dust
but go to the country, like Palawan or Cebu
otherwise you'd suffer with diesel's smell and smog in the city
though the city is perfect for shopping :D