Searching apartment or else (1 month staying)

Hello everyone, we are two university students, from Italy.
We are going to stay in Korea for one month ( plus 3days) to attend a one-month course of Korean language.
There is just one problem( and big), we don't know where to stay.
We've looked around for homestay, guest houses and ect but they was quite expensive.
Our idea is NOT to spend more than 500000 won a person, for one month staying. I mean, we are students...and we don't have so much money....if we can we want to save money as much is possible.

Our school is near Sincheon station and we want to find a place around this area. We would like to stay in a studio apt. or in a loft, with a kitchen and a bathroom.

We've asked our friends and some of they said that it's a bit too early to find where to stay in July...we could find something later in June.
Is it true? 'Cause we think that is quite late, that's why we are worried about all this.

Can anyone help us? or just give some advice...
Thank you,

Chiara & Vivien