The following gives me a headache, because "pavilion" has been used in the end twice. How to edit it?
One day we went into the Heng-yang Mountains, where there are traces of a famous pavilion called "Rub-the-mirror" pavilion, which perhaps interest you to hear the story of that pavilion.
I'm a journalist, not a teacher, and this is one way I might edit it:
"One day we went to the Heng-yang Mountains, where one can find traces of the famous Rub-the-Mirror Pavilion. You might find its story interesting."
The original sentence doesn't indicate whether you actually saw the traces of the pavilion or simply visited the mountains where the pavilion is located. If I knew that you saw what's left of the pavilion, I might change the first sentence to read:
"One day we went to the Heng-yang Mountains and saw the remnants of the famous Rub-the-Mirror Pavilion."