The statute requires that notice of the public hearing be "published". Is it enough to post the notice on the city's web site?

No. G.S. 160A-101(7) provides that whenever the word "publish" is used in Chapter 160A, it means "insertion in a newspaper qualified under G.S. 1-597 to publish legal advertisements in the county or counties in which the city is located." Nothing bars the city from posting the notice on its website, but it also must always publish the notice in a qualifying newspaper.