I Plans to Hang Out with My Friends for A Day.

My plans are the following: below.
First, we will go window shopping in Taipei and have lunch there. And then, we need to will take a taxican  to the National Palace Museum make us know some cultures about Taiwan and learn about Taiwanese culture. And next, we will take a bus to Yangmingshan and sit on the grass to have and eat dinner while enjoying the night view.
After a while, we can could take a walk and lie on the clean grass to see the stars. Finally, we could also can go to the night market to have some midnight snacks if you we want to do.

Good effort! It sounds like a fun day. 

When you speak of future plans, you use "will" + verb

"Could" suggests possibility while "can" suggests ability

I My Plans to A Hangout with My Friends for A a Day.
My plans are the following: below.
First, we will go window shopping in Taipei and we will have lunch there. And then, we will need to take a taxicab to the National Palace Museum to learn about Taiwan's culture. And Next, we will take a bus to Yangmingshan, sit on the grass to while having dinner and enjoy the night view. After a while, we will can take a walk and lie on the clean grass to see the stars. Finally, we also can also go to night market to have some midnight snacks if you we still want to. do.

Very Good!

I Plans A Hang Out with My Friends for A Day.

My plans are the following below.
First, we go window shopping in Taipei and have lunch there. And then, we need to take a taxicab to the National Palace Museum make us know some cultures about Taiwan. And next, we take a bus to Yangmingshan and sit on the glass to have dinner while enjoying the night view.
After a while, we can take a walk and lie on the clean glass to see stars. Finally, we also can go to night market to have some midnight snacks if you want to do.