There are three different groups of libraries in the valley, Salt Lake City, Salt Lake County and one independent library in Murray. Here are links to each of them:
Salt Lake City Library System
Marmalade Library (Opening Fall/Winter 2015)
Salt Lake County Library System
Bingham Creek Library in West Jordan
Calvin S. Smith Library in Salt Lake City
Columbus Library in Salt Lake City
Holladay Library in Salt Lake City
Hunter Library in West Valley City
Ruth Vine Tyler Library in Midvale
Whitmore Library in Cottonwood Heights (Closed until autumn 2015 for remodeling)
Sippy Cups & Chardonnay 