First the info of Viator of going back to Seoul , 5.20pm is wrong. The time should be at lest 7:30pm. It takes 6 - 7 hours both ways. There are different hiking routes in Mount Seorak. May take one of them. If not, take a cable car and do some walking up to one of mount top and then visit the temple. There is small museum of the temple, free for visit. Naksansa Temple is famous for the Seawater Koon-yim
Good view of a seaside city.