My friends and I found out that it costs around $100 to fly for an hour to Jeju Island from Seoul, so of course, we did just that. We spent three amazing days on the island- wish we had more time! Didn't realize how big the island was until we tried to go from point A to point B. We initially booked a rental, but didn't realize we needed an International Driving Permit till we tried to pick up the car. Friends, take note if you ever need to rent a car internationally! Thankfully the taxis we're abundant and the bus was easy and affordable to ride.
If you don't have much time on the island, I highly suggest devoting yourself to a beach day- you have to enjoy island life after all. My favorite beach is Hyeopjae- known for the clear clear waters and shallow waves. I loved it so much that I went twice. And saving a day to visit the green tea fields. I went to the fields at O'Sulloc tea museum/Innisfree Jeju House (tip: bring your passport for duty free shopping and try the green tea desserts at O'Sulloc, you won't be disappointed). And if you're lucky, making sure to take in all of the island with a hike (wish I had time to this, there's so many hiking trails).
For food, make sure you eat the island's delicacies: abalone and black pork belly. And of course, all the fresh seafood dishes. The top two restaurants I recommend are Samsanghyeol Haemultang for loads and loads of fresh seafood in a spicy broth with ramen and Donsadon for black pork belly (G Dragon and many other Korean celebrities frequently dine here apparently). There's sooooo many restaurants that serve fresh sashimi and abalone, so I can't say which particular one to go to, but you will be disappointed if you don't eat these delicacies straight from the island.
Hoping to go back again one day!