Housing in Busan
There are plenty of websites, unfortunately with many the properties they advertise don't exist or have since become unavailable, but are used as a lure to get you through the door.
Usually your best bet is to find somewhere where you might want to live and hit the local 부동산 BuDongSan offices around there.
Here is Navers real estate site to get you started. (requires Korean) It's already linked for Busan officetels so just click on the Gu then dong that you require.