My legs were the first place I started. But I have this like designated carved in box that I stick too. Well obviously that ran out of room quick. So i've moved up my legs. Like one of the previous posters stated - its pretty difficult to cover with shorts/bathing suits but I don't often wear either and found that as long I cut higher up. I'm okay with it.

I've never cut my wrists so I can't compare the two, but I find its a lot more private to do the legs. Either way be careful because there are some pretty important veins in those areas as well.