First trip to Korea!

Hi all! My partner and I are visiting Korea and I’m hoping for some recommendations on where to go during my visit. I’ll be staying for about 9 days (15 - 24 dec) and here are a few things I am planning to do:

1. Lotte world
2. Hiking at Deogyusan National Park
3. Skiing (not sure where yet)
4. Ice skating

As there are way too many recommendations online (especially TikTok) on what to do and where to go, there have been mixed feedback on popular places and it can get pretty overwhelming. I would like some recommendations especially for places with beautiful sights to see or interesting places to explore!