What places did the Mariner stop at in "The Rime of the Ancient Mariner"?
I am unsure of what you specifically mean. Are you referring to the life of the Mariner after his experiences? Part of the penance that the Mariner must pay for his crime in killing the albatross is that he has to wander the earth, sharing his tale with those that he feels compelled to share it with. Note how the Mariner himself describes his plight:
I pass, like night, from land to land;
I have strange power of speech;
That moment that his face I see,
I know the man that must hear me:
To him my tale I teach.
Therefore, in a sense, the Mariner does not stop at any place. He is compelled to wander the world, "teaching" his tale to those that he feels directed to share it with. His experiences have transformed him into a restless wanderer, giving him "strange power of speech" and ensuring that the lesson that he has learned through what he has done will never be forgotten, and so that hopefully man will have a proper relation with nature that is not based on exploitation or abuse.