Yes it's safe to eat an egg everyday if you want too or even eat 3 or 4 eggs per day if you'd like too.
I eat 2 eggs every morning for my breakfast along with either bacon or sausage and I've stayed very healthy.
Eggs are very good for your health as well so eating eggs everyday can provide you with many health benefits.
Although eggs contain 212 mg of cholesterol per one large egg the cholesterol that the eggs contain will actually help with your good cholesterol levels.
So eating eggs won't raise your bad cholesterol and eating a few eggs per day is a healthy breakfast.