Bank ATMs can offer some of the best available exchange rates for travellers.  Although you may find more convenient currency exchanges in the airport, hotel, and even little old ladies on the street, that convenience comes at a premium in the form of less favorable exchange rates.  If you're lucky, you may be able to find a street exchanger willing to bargain. There are money exchange stores in all the touristy places. Their rates are way better than the hotels. Korean banks also have good rates.

Some Korean ATMs have funky hours and may not be open 24 hours a day.  Also, keep in mind that many have a very low cash withdrawal limit .  The airport and certain other ATMS are 24 hours a day, but most others are highly restrictive so make sure you take out enough money when you do hit an ATM. 

Your best bet when travelling internationally is to find a local branch of a large, multinational bank (e.g. Citibank, HSBC, Chase, etc.).  They are less likely to carry weird, "hidden" fees, will likely have comprehensive English menus, and if you have a domestic account with them, you may get a discount on international transaction fees.