Even the fashionable apartment complexes in areas like Apkujong and Kangnam are soulless hutches, built for property speculator's profit rather than the comfort of their residents. The problems of the Korean construction industry were recently revealed to the whole world after the Sampoong Department Store tragedy. Not that you have any say in your choice of housing, just look around to see that everything looks in order. Seoul can appear very misleading. Most Part-timers stay at yogwans, which are the Korean equivalent of Japanese love hotels and while there are literally thousands of these all over the city, only a very small number will entertain the idea of foreigners looking for long term accommodation.
Facilities range from pretty awful to non-existent.
Your students might be appalled to learn that you actually live in a Yogwan as they have sordid reputations. If you are living in a Yogwan then be careful about telling your students, they are the haunts of sinners and criminals in their eyes and you may lose valuable respect. Check out the Lonely Planet guide for a really good list of Yogwans, but here are a few comments of my own. Rates are 400,000 to 450,000 per month but this includes things like private bathroom, phone, TV etc., there is even a washing machine downstairs. The owners are wonderfully friendly but do not speak English.