Here's a list of items that I packed for quarantine! (Keep in mind that every quarantine facility is different) For reference, I stayed at one of the government facilities (Grand Hyatt Incheon Hotel).
2,000 KRW or Credit card: If you are staying at a government facility, you will not have to reserve a spot beforehand. But you'll need this to pay for your facility as soon as you enter the hotel you are assigned to. I have heard that they also take USD but I am not 100% sure about how correct this is.
SIM card: You'll need a Korean phone number for a lot of things, including your "Korean Contact". I had mine shipped to me before I arrived in Korea (Premium Classic Plan on Trazy)
Electric Hot Pot: To heat up food/cook meals. The meals often come quite cold, many students have wished they brought one.
Snacks!!! Lots and lots of snacks! The meals can get quite repetitive so it's good to have your own snacks to switch things up a bit and help with boredom (;
granola bars, gushers, chocolate, Hurricane popcorn (the pre-made kine, not the microwaveable one)
Easy cook meals: Easy cook oatmeal, easymac, ramen, etc.
Amazon Fire stick
At least two weeks worth of clothes: You can wash your clothes but it may be hard to dry. Since my windows did not open, my clothes did not dry well at all when I have tried to wash them. Make sure you have some comfortable outfits to lounge in especially!
Two towels: The hotel gave a couple but I brought just in case since I didn't know how much they would give
Adapter AND Converter: Note that an adapter just changes the shape of your plug, while a converter changes the voltage of the energy when you charge your devices (120 in America, 220 in South Korea)