It is really safe, I have been there 3 times in just 2 years. I must say that the Tourism board is doing a really good job in promoting and making people feel safe and taken care of. There are buses that takes tourists around major sightseeing places around town at minimal cost. Also, there are tourist information centers around where you can book day tours and enquire.
Also, with the influx of foreign tourists due to their booming entertainment scene, most people (really not difficult to find in the cities, esp Seoul) can understand basic english and chinese.
Fyi, for all three times, I have gone on free-and-easy travel. ((: