Start with the main branch, then on to the various neighborhood branches. It’s important to pick a section you are interested in beforehand. Fiction might be too overwhelming, so I’d go for the math or computer technology sections.
Once you’ve done this in multiple cities you can compare the sizes of those sections between different cities and how current the books are, i.e, for tech books, do they have books on the latest trend in programming languages.
Go to coffee shops and bakeries in between. I can usually squeeze in the main branch and one or two neighborhood branches in a day. Research the city to figure out which neighborhood libraries to go.