A week in Seoul

Hello everyone! I'm coming to Seoul for the conference and was wondering what are the best things to do and see there. I'll be at the event on Wed-Fr, but stay for Saturday to explore the city. Not much time, but all more reasons to see the highlights.
I'm into museums and markets, I love exploring local food, so any tips will be very much appreciated.
Is it safe to wonder around alone? Are there any particular areas to avoid? i know things are quiet in Seoul, but it is a big city, so I'd like to come prepared.
Thank you very much!
ZZ