Although culturally, Korean people often go out for drinks, hiking expeditions, or travel with co-workers, I have seen Korean people bow out gracefully from these requirements. I'm not saying that you should refuse to attend any outings with your co-workers, but it may be okay to miss a few or, at least, leave early. Attend most of the activities, but don't feel stressed about attending them all. You can also try to skip a particular type of event. For example, if you are a non-drinker, you can try to skip a few of the events that center around drinking. If you are allergic to seafood, perhaps you can try to skip visiting a seafood restaurant with your co-workers.
Try to incorporate your new Korean friends and co-workers with your hobby. If it is feasible, you can try to teach your Korean friends your hobby or invite them to participate. This will go a long way in solidifying relationships in your new country. You are also combining time spent with your Korean friends and co-workers with time spent doing what you enjoy.
Set aside time after work to do what you enjoy. Set aside some time so that your time is not swallowed up by work. You can spend an hour a day or an hour a week. Setting aside just a little time can go a long way towards making you feel more balanced and enriched. Try not to talk yourself out of the time that you've set aside. In short, don't deviate from your schedule.
If your schedule fluctuates, create a "to-do" list with time set aside to work on your hobby. Therefore, you are not obligated to work on your hobby at a specific time, but anytime during the day or week if you make a weekly "to-do" list. You can also create a list that divides your tasks between things that you want to do and things that you must do. For every few tasks that you must do, you can reward yourself by doing something that you enjoy.
Use a timer to help you manage your time if you are seriously under a time-crunch. You can set your timer so that you complete a task within 30 minutes, giving yourself another set period for working on your hobby.