I came back home <strike style="background-color: rgb(255, 255, 0);">in</strike> to Tokyo from my hometown.
Since most people who <strike>spent</strike> spend time in their hometown usually come back to their homes on the second day or third day of the year, heavy traffic jams occur around Japan.
Sure enough, I was stuck in<strike>to</strike> a traffic jam on a freeway today.
However, I was lucky because I could see one of the most beautiful pieces of architecture in Japan.
It's Tokyo Station.
The terminal of the freeway bus is Tokyo station.
Tokyo Station is famous for its historic brick appearance.
Although the station has been restored for around three years, the restoration was completed shortly before.
I took <strike style="background-color: rgb(255, 255, 0);">a</strike> the picture below after getting off the bus.


***Notes***
When you wrote: 
"...most people who spend time in their hometown usually come back to their homes on the second day or third day of the year..."

You can also say: 

-most people who spend time in their hometown usually come back home on the second day or third day of the year

-most people who spend time in their hometowns usually go back home on the second day or third day of the year

-most people who spend time in their hometowns usually go back to their homes on the second day or third day of the year

When you wrote: 
"I took the picture below after getting off the bus."

You can also say: 

-I took a picture after getting off the bus, which is shown below.

-Below, you can seen a picture I took after getting off the bus.
-Below is a picture I took after getting off the bus.

Tomorrow is the first work day of the year. Time flies. It's the first time in so long, I <strike style="background-color: rgb(255, 255, 0);">have</strike> visited the first shrine with my family today to pray for their safety and happiness. Same as usual, I have to strive to speak and listen (to) English this year (<strike>, </strike>) too. At first, I will try to enjoy communicating with co-workers from abroad even though my English hasn't improved a lot. I look forward to <strike>being</strike> <strike style="background-color: rgb(255, 255, 0);">stimulated</strike> (learning) through conversation with them.

***"Stimulated" is a strange word choice.*** 
Did you mean: "learning"?
You can also use "getting better", "improving", "making progress in my English" 

The first diary ("my first diary" or "first diary" is a better title, sounds more natural)

I caught a cold so I slept at home. 
Someone who can speak a little Japanese whom I teach English.  I don't really understand the meaning of this sentence. Are you trying to say something like: If someone can speak a little Japanese, I would like to be taught English by them? (誰かが日本語をちょっと話せたら、英語を教えられてほしい) my Japanese is not too good, but something like that?