I love the Phoenix public library system. The staff at the Mesquite branch helpful and the selection is good. You can always order what you want from another branch and it will arrive in just a couple days. The seating is comfortable if you want to relax for a bit with a book and there are plenty of tables if you need to sit down and get to work. There are also a fair amount of computers available for use if needed. Check out is a breeze if you do it on your own or there is someone to help if needed.
Check their schedule they offer some interesting events at this location from time to time that are family friendly, especially during the summer.