Genuinely, the crime rates in South Korea are pretty low. Even in Seoul, girls can walk back home at night as long as they don't use any dodgy looking dark alleys, which blatently says "don't go there".
My mother lives here and she is Korean, so I would most definitely know if theres any crimes going on.
I would think in Geoje, it is pretty safe. But as always, I would recommend you to be logical. As one says, it's better to be safe than sorry :)
I've heard there are occasional break-ins in houses, I guess this will depend where you are living. If you live in an apartment, you should be pretty safe (plus they have concierge/guard). But if you do live in an individual house then, just like anywhere else in the world.
Anyways, I hope this helps and feel free to ask any other queries!