I lived in korea for over ten years and i must say its a wonderful place to be. very beautiful. you will be i pyeoungtaek which is about a 15-20 minute drive from the osan airbase and this afb is a decent size. the bx is one of the biggest on the peninsula. if youlike to shop, right outside the airbase is a shopping center and shopping in korea is amazing because u get to haggle and pricesare cheap.
i would recommend seeing any traditional korean places. go to the mountains.
you are about an hour away from seoul which is the capital of korea and its also one of the biggest cities in the world. have fun!! if u go to yongsan, there are several amusment parks, and many many shopping districts such as itaewon, myongdon, dongdaemun.
try all the food, some you wont like but some you will fall in love with. try the samgyupsal and or bulgolgi these are two types of meat that are absolutely delicious.
i must say im jealous, i plan on going back someday.