Some people love going to the coffee shop to relax (i.e. the mob at Starbucks).
I love going to Tempe Public Library to rewind.
It is bright, clean, and reasonably quiet. It has amazing book/magazine collections, lots of family-friendly programs, and helpful staff members.
The Connections Cafe inside serves really good scones. There is a $5 minimum for credit cards I think.
Although there was at one point in 2013 some technical problem with renewing books online and as a result I was wrongfully charged late fees for a couple times, I think for the most part Tempe Public Library a true blessing to the community here and offers wonderful resources.