A Trip Through the Middle of the U.S.  [1]

The best parts of the U.S to me are the national parks. I enjoyed the pure hiking experiences in Glacier National Park in Montana, the exciting rafting trip in Grand Teton National Park, and the extraordinary geographic features in Yellowstone National Park.

Two years ago, when the Delta plane landed in Salt Lake City, I knew that my trip had started. [2] Three of my friends and I rented a Recreational Vehicle (RV) in this Mormon city in Utah, and directly drove 10 hours to the entrance of Glacier National Park. After a week's hiking, on over 10 trails, with 10 miles a day on average, we headed back to Yellowstone. There's an "8"-shaped route in this park, so we began from the north entrance, travelled in an [3] "S"-shape, and exited from the south entrance to Grand Teton National Park. We spent eight [4] days in these two national parks, and two [4] more days in Salt Lake City, before we finally caught up our flight back to New York. Being a long, fun, and interesting trip, I think I should record something for us.

In the next few notes, I'll attach more details. See you then!
(I hope someone can help me to make my writing more natural. Thanks! )

[1]  Capitalize the first word and the "important" words in a title.  Unless it's the first word, you don't capitalize "the," "a," or prepositions.

[2]  The past perfect tense is usually appropriate when when we mention an action that happened before ("had started") another action ("I knew.")

[3] "S" begins with a vowel sound:  ess

[4]  Many textbooks say it is better to write out the numbers one to nine in words (unless, of course, you're doing math).  But don't worry about it. Many people ignore that rule. 

Excellently written.  What you wrote already sounds natural.  A reader could easily think it was written by a native speaker.