I first read about this bookstore in a list of the 20 most beautiful bookstores in the world and so I had to see it when I was in LA.
It’s located in the heart of Downtown, on the corner of 5th and Spring Street, in an old bank building. They mostly sell used books and you can even sell yours there, which is very rare these days. Additionally they host many events, such a readings and book signings, open mic nights and concerts. The name refers to the problem of physical bookstores closing due to the impact of Amazon and e-books.
More information on thelastbookstorela.com
Other beautiful bookstores: Lello & Irmao in Porto, Portugal Ler Devager at the LX Factory in Lisbon,Portugal Housing Works Bookstore in SoHo,New York City
Big Cities. Bright Lights. 
I like this. I have switched to the Kindle, but
I love bookstores