Beijing travel

Last month, I visited Beijing city. I went there by train from Shenzhen. It took 24 hours.
The weather there wasn't bad, I can see blue sky with no problem. Although the temperature was low, about minus 6 degrees, it's what we call a "dry cold", which actually is not very cold. On the contrary, wet cold can be rather cold even if you are wearing thick clothing, it's a freezing cold which makes you feel very uncomfortable. Cities like Shanghai have a wet cold.

Now, I am coming back to Hong Kong, and will be staying until the 19th of January. I will travel to London first and then LA, America for my internship.

Notes: using "city" after Beijing is correct but not really necessary.

Instead of saying "LA, America", I would just use Los Angeles.

I removed "here" from the last sentence because "coming back" sounds like you are writing this in transit; while "here" says you are already in Hong Kong. The change was simply to remove the slight contradiction.  You could also use "returning to Hong Kong".

Very good.