Yeshurun is one of the older synagogues in Jerusalem. Located on King George St., it was once one of the cultural centers of the city. Now, on weekdays, you can usually find an equal number of congregants and of their attendant SE Asian caregivers.
Adjacent to the synagogue and one floor up is the Yeshurun library. It has a nice range of books, and was once a meeting place for scholars like Shraga Abramson. I once read a description from the sixties, of how the librarian would take orders for books the library didn't possess. Then use his lunchbreak to travel over to the National Library and borrow them on his own name, so that in the afternoon he could present them to his readers. The library contains, among other things, books from the libraries of R Yissachar Dov Ritter of Rotterdam and of SZ Shragai, the Religious Zionist leader (including at least one Vonnegut novel).
In recent years the library has become moribund. One year, on the night of the Pesach Seder, a group of knowledgable thieves broke in and stole all the Venice printings. Beit Morasha, which used the premises of the synagogue for several years, has moved and has its own library now.
But nevertheless, the Yeshurun library is worth a visit. The librarian is a deeply knowledgeable and dedicated professional. The atmosphere is unique, with a blend of Beis Yaakov girls (whose school does not allow them access to most public libraries), aging scholars and curious Jerusalemites. And there are still gems hidden among the books - annotations in the hands of noted rabbis, obscure editions and a very rich collection of books on Eretz Yisrael.