This is factory the one you visited.--WRONG可以改为：This is the factory,the one (that) you visited./This is the factory - the one (that) you visited.
For many cities in the world,（ ）New York is an example,...句子没有完,不好判断,但是 我倾向于用A.an example of.有这说法
This dictionary has many examples of how verbs are used.例证
She brought along several examples of her work for him to look at.
样品