It's famous for cherry blossoms, autumn leaves, bamboo trees, and temples.

This sounds more natural in the US.

When I visited there, there awere junior and high school students on a school trip, and people wearing kimonos.

US alternative

If you ride the Sagano Romantic train, you can seerelax while seeing the nature and beauty of the valley relaxingly.

US alternative

Arashiyama is one of the many sightseeing spots in Kyoto.

If you are specifying one sightseeing spot you should probably emphasize that there are many sightseeing spots and you are going to be talking about this one in particular. For example, you could also say, Arashiyama is a nice sightseeing spot in Kyoto.

In addition, there are many shops at the foot of the mountains, so you can enjoy food or shopping.

I have never really heard foot of the mountains in usage. Foot is singular so I believe that mountain should also be singular and not plural, so you need to match the case.

When I visited thereArashiyama, there awere juniormiddle and high school studenters on a school trip, and people wearing kimonos.

Since you are talking about the past tense, you need to use were instead of are. In the second half of the sentence, you are talking about people (as in plural), so you need to match the case. Kimonos, not kimono. I was a bit confused by what you mean by junior and high school students. Did you mean middle school students? Or did you mean junior high school students?

If you ride the Sagano Romantic train, you can see thleisurely see nature and the beauty of the valley relaxingly.

So I would say that leisurely is the word you would probably want to use here. Also, usually adverbs come directly before the verb.