There are only a handful of movie theaters located outside of downtown, but surely more will be built soon.   Downtown there are two very large theaters, Hanil Gukjang and the Joong-ang Cinema.  Both of them are set up sort of Western style, which makes it very easy for foreigners to use them.   They have multiple screens and shows start at about 10:30 at the earliest and on weekends there are usually late showings around 11 or 12.  During the week the 9 p.m. showing is usually the last one.  In the future I will try to make a map just to direct you to the theaters.   There several budget theaters, where tickets are 4 or 5,000 won instead of 5,500.  These theaters will show sex films some or most of the time, depending on the location.   Normal first run theaters are:
 

The others are all second run/cheap or sex movies.  In case you didn't know, Korean theaters have assigned seating.  Check your seat number, cause your fellow patrons will be really uncomfortable to get you out of their seat.   When buying tickets ask for the show number (as in first show of the day, second show of the day) like this:  "Sa-hwae du-jang ju-seh yo"  (Please give me two tickets (du-jang) to the fourth show (sa-hwae).  Usually there is a different window to buy tickets to each show, so line up with the poster for the show you want to see.