I've known directors that didn't say anything. Others that announced it because the district was so bad they wanted everyone to know. And others that left because of personal reasons and just said that.
So it depends on you and your relationship with those kids and district.
Personally I say goodbye but I've learned my lesson from the first time I left a job. Kids get attached sometimes. So I keep it short and to the point and always support the next director who takes my place, no matter my feelings. My leaving isn't meant to make anyone's life harder. It's just a change we all have to get use everyone to.