"In the House of the Seven Librarians" by Ellen Klages

First appeared in Firebirds Rising, an anthology of children's fiction. It was up for the Locus award. Reprinted in two year's best anthologies by Jonathan Strahan, Ellen Datlow, Gavin J. Grant, Kelly Link, and Rachel Swirsky did the audio. 

This story positively oozes charm, a Klages specialty: protagonists you care about. Bonus: a cool speculative library.

The beautifully built Carnegie library is abandoned for new technology. Seven librarians are left behind with this forgotten library and one day a child is left with them. She grows up among the spinsters in a library that fulfills wishes (a teddy bear, if well used), hides readers in alcoves that disappear later, and bends time (or maybe the librarians aren't especially good at monitoring the days--they celebrate the fourth of July during a snowstorm).

The story doesn't gather steam until the librarians want to hand the keys over to the new girl as another retires because she cannot reach the shelves any longer.  But she wants to witness the world before taking over, first.