Generally, a lot of schools within SMOE do not provide the key money. Key money in Seoul usually range from 5 to 10 million WON with 3 million on the lower end.
With that being said, when I worked for SMOE (finished last week), my first place was just miserable. Internet was really slow and the mold was a constant problem. I managed to endure it for 2 years but decided to move my last and third year. Instead of taking the housing stipend, I decided to talk to my school about moving to a new place. I was nearing my 2nd contract, so breaking housing contract wasn't an issue. I ended up finding a nice officetel which accepted my school's responsibility over me and decided not to take any key money.
Anyways, here's some advice about finding housing in Korea.
1. Key Money
Nearly all places here require key money and usually, it starts from 5 million to 10 million. There are a few places that take 3 million but not that many. Currently, your school is under contract with the landlord, however, if you take the housing stipend, the housing will be under your name. This means that they will definitely require key money from you. My school was able to sign a contract without the key money because they can be trusted while we're just foreigners.
2. Cancellation Fee
The cancellation fee depends on what's written on the housing contract with your school and landlord. I know my previous landlord told my school that if I were cancel the contract mid-way, he would charge me one month's rent, which I would be responsible for. This is something you'd have to check with the school.
3. Real Estate/Broker Fee
Yes, usually the fee ranges from 250-400,000 WON. It depends on your rent and key money. Sometimes, you can bypass these real estate agents if you directly sign with the landlord. If you have a Korean friend willing to help you find housing, this can be done. However, most of the time, landlords go with real estate agents.
4. Short-term Contracts (단기임대)
I'm not sure where you are located but there are places in Seoul, especially Gangnam-gu and Songpa-gu that offer short-term contracts. You don't pay any key money besides the a month's rent in advance. However, most places even with key money take the first month's rent with an additional month's in advance. You just don't pay the last month. Usually, these places are pricey though. The contract starts at 3 months but you can sign for a 3-6-9-12 month lease. A lot of times, if you want one year, these places will offer a 6-month lease and let you extend every 6 months. Anyways, these places are usually starts at 600,000 WON per month. Songpa-gu is usually starts at 800,000 WON per month. They are usually fully furnished and are very comfortable.
Unless you have 5-10 million WON at your disposal, finding a new place will be difficult. There are places in Itaewon that offer decent prices but a lot of them require key money too. Your best bet in saving money would be asking the school to help you instead of taking the housing stipend. The housing stipend is 200-300,000 smaller than the housing allowance. If you talk to your school and express legitimate concern, they can help you find a new place under their name. This means, you still get your 700,000 WON for housing since it's under your school's name. Go with your coteacher to real estate agents and try to negotiate the terms that the school will take full responsibility for any breaking of the contract. This is, of course, at the mercy of your school. Seems like you're new to the school and it might be a little difficult to persuade them this early on.
However, if you insist on getting the housing stipend then you will have to prepare yourself in obtaining key money or going into those expensive short-term contracts.