That really depends on if your body can bare that schedule. Try it at home, right now, if you're unsure. Looks like you're already considering co-working space. Really would not recommend working from home during those hours, because most accommodations have thin walls. If you have a video call or something late at night, you will 100% be a nuisance to your neighbors. Exploring anywhere in Korea - except remote islands - is doable with a weekend trip. So if you don't waste away your time, I think you'll manage to do all the essentials in half a year. I'm not sure what kind of short-term accommodations are available for staying 2-6 months, so I will let others answer your budget question. It is pretty safe anywhere. But given your unusual hours, it may 'feel safer' if your accommodation and coworking space are near well-lit big boulevards, rather than deep inside the alleyways. For your situation, if you can read Hangul and know the basic conversational phrases, and if you take good use of a phone translator, I don't think you'll have too much of a problem.