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Hiking is sort of a national sport in South Korea and on a weekend with decent weather in the average national park/hiking spot you will most likely not encounter 5 minutes without encountering lots of fellow hikers.
A good starter would be Korea4Expats
Every weekend, Seoulites of all ages head out to the hills and mountains that surround the city. Autumn is a particularly popular time for hiking. While Seoul is not as well served with parks as cities in some other countries, the city and its immediate vicinity have a wealth of hiking trails. Sundays are especially crowded as that is the one day almost everyone has off work/school.
and they also point to some of the obvious choices should you wish to go with a group: Hiking Groups aimed at the English-speaking (unfortunately the article is as of 2013 and the links listed are down, they list emails you could try in case).
Instead I found a list of very active groups on Meetup.
New comers are more than welcome, definitely! for novices, beginners, moderate, and advanced hikers.Please, don't hesitate because you're alone. Most of us come alone and all get along together.It is a social club made up of various kinds of people.