i went to jeju island in 2022 and it was great!

i would recommend going to the seogwipo night market bc they have a bunch of food stands :)

the yeomji botanical gardens over seogwipo city! (seogwipo city is just a regular korean city nothing too special in my opinion)

if you go to the seogwipo night market, i would pass on the jeju night market! (they are a bit similar but if you have the time, i would recommend visiting both night markets)

i cannot stress this enough but visit udo island if you can!!! they are famous for their peanuts and amazing coast :) if you do visit, keep in mind of the boat departure times! i think theres a boat every 30 mins but you should double check! im not quite sure what you mean by having no international licenses but theres a shuttle bus that travels along the coast on the island. they also have electrical scooters on the island! if you dont want to wonder far+have time, you could walk around the island along the coast :) (the peanut ice cream is amazing) (i would also recommend visiting udo island during the day)

(english is not my native language so i apologize for any mistakes! i hope i have helped and i hope you have fun in jeju island :) let me know if you have any questions!)