Are there any public libraries with a fair number of English-language books, near BTS stations if possible?  And would be great to find one with magazines and newspapers like New York Times, Financial Times, Time, National Geographic, etc. Thanks.

https://neilsonhayslibrary.org/

English collections within library structures a far a few between.

Chulalongkorn University and Chiang Mai University Libraries probably offer the best selection of English inventory and a wide variety of current periodicals. 

 

Outside of the library thing, you might be interested to know that Bangkok and Chiang Mai have numerous exclusive English bookshops of all flavours - ranging from well known to holes-in-the-wall, where one can find new and used reading material as well as the odd periodicals/journals.

Both the British Council and A.U.A used to have English book libraries. Don't know if they still do.

It interested me as well, so I did a google search and found this

 

https://en.wikipedia.org/wiki/List_of_libraries_in_Thailand

 

https://en.wikipedia.org/wiki/Neilson_Hays_Library