Where can I find the newspapers such as New York Times, the Wall Street Journal or even Los Angeles Times? I want to read the paper edition there sometimes. Thanks in advance. 
There used to be a gift shop in the then-called Taipei Hilton that sold foreign newspapers before it was reburbished, it’s gone now.
Try gift-shops in other international hotels, or Eslite. Sorry I can’t be more specific, I haven’t looked recently to see if they have them or not.
Caves used to have some. Zhongshan N. Road.
I was in the new Eslite on Sunday. They have the weekend Financial Times which is not a bad read 95NT$. So I would guess maybe it is printed here. I would think the NY Times if found is outrageously expensive. In Tokyo it is 3 days old when it arrives and the Sunday NY Times is 42USD!
I would stick to on line reading. www.aldaily.com has all the papers and magazines as well as articles of interest in one place.
Have you tried Page One?
Subscibe to the International Herald Tribune. It is printed here in Taiwan and arrives at your home before 7:30AM Mon-Sat. Here is the URL iht.com/subscriptions/index.php NT$34 per day with a 12 month subscription. It is owned by the NY Times. Great substitute while living abroad.