Jeju is an island. We can go to Jeju by plane. Jeju has two cities, Jeju, and seogwipo. I’ve been to Jeju about three  or four times. Jeju is famous for mandarin. Jeju is fun to go when it doesn’t rain. I like Jeju because it’s a good place to relax.  

  Student's sentence            Corrected sentence            Grammar explanation          Better sentence     

Student's Sentence: Jeju is an island.
Corrected Sentence: Jeju is an island.
Grammar Explanation: The sentence is correct. 
Better Sentence: Jeju is a beautiful island in South Korea.

Student's Sentence: We can go to Jeju by plane.
Corrected Sentence: We can go to Jeju by plane.
Grammar Explanation: The sentence is grammatically correct. 
Better Sentence: The easiest way to get to Jeju is by plane.

Student's Sentence: Jeju has two cities, Jeju, and seogwipo. 
Corrected Sentence: Jeju has two main cities: Jeju City and Seogwipo.
Grammar Explanation: Capitalize Seogwipo. Use Jeju City instead of just "Jeju" to avoid repetition. A colon works better when introducing a list.
Better Sentence: Jeju has two main cities: Jeju City and Seogwipo.

Student's Sentence: I’ve been to Jeju about three or four times.
Corrected Sentence: I've been to Jeju about three or four times.
Grammar Explanation: The sentence is correct.
Better Sentence: I've visited Jeju about three or four times.

Student's Sentence: Jeju is famous for mandarin.
Corrected Sentence: Jeju is famous for its mandarins.
Grammar Explanation: Use its to show possession. Mandarins should be plural because it refers to the fruit in general. 
Better Sentence: Jeju is famous for its sweet mandarins.

Student's Sentence: Jeju is fun to go when it doesn’t rain. 
Corrected Sentence: Jeju is fun to visit when it doesn't rain.
Grammar Explanation: Use visit instead of go after "fun to" because it sounds more natural.
Better Sentence: Jeju is more enjoyable to visit when the weather is sunny.

Student's Sentence: I like Jeju because it’s a good place to relax.
Corrected Sentence: I like Jeju because it's a good place to relax.
Grammar Explanation: The sentence is correct.
Better Sentence: I like Jeju because it's a peaceful place where I can relax.

Better Paragraph
Jeju is a beautiful island in South Korea. The easiest way to get there is by plane. It has two main cities: Jeju City and Seogwipo. I've visited Jeju about three or four times. Jeju is famous for its sweet mandarins. I enjoy visiting Jeju when the weather is sunny because it's more fun to explore. I like Jeju because it's a peaceful place where I can relax.