That really depends on where you are. Not too difficult to find these in major (1th, 2nd tier) cities but a bit more difficult in smaller cities and in the west of the country. 

Look in any larger book stores that might have foreign books. Most likely these also have some magazines or newspapers. This goes for the English book store in Guangzhou's Books building in Tiyu xi anyway. 

Otherwise a lot of newspapers and magazines can be found online these days. 

You can go in Western food shops (easy to find in fancy cities), they often have magazines and newspaper in English.

I didn't buy newspaper longer than 20 years. I read everything online for free.

Why would I buy newspaper, if I can click on any World-ly newspaper, and read it on my puter with my slippers on? I don't even need to exit my house.

Just enter the newspaper's title in search, bookmark it, and 'read yourself out'.

For some papers, you must pay online subscription, as WSJournal or Telegraph (10 articles for free per month).

After I'm done with 10 articles, I still open Telegraph daily, copy the title I want to read, and paste it in the search.

Find another newspaper, which publish the same article for free.