I spend a lot of time in libraries. They serve as my office. Here are some thoughts on how to find a library that meets your needs.
You can start your research online. Google up library information for an area you are interested in. I like looking for a library system where some branches are open 7 days a week. I have also found that if their shortest day is 5 hours instead of 4, that helps make sure I can keep charged up.
You may also be able to find information online concerning things like number of public PCs and usage policies. Some libraries are more flexible than others.
But some information cannot be found online, such as how many outlets are available and how friendly the staff is. Some library staff actively look for BS excuses to evict homeless individuals. Others are genuinely supportive and considerate.
So, at some point, you need to physically go to different branches and see how well it works for you.
If you have a laptop, tablet or smartphone, you should be able to plug in (assuming they have outlets -- some do not) and use the Wi-Fi without a library card. You can also read books without checking them out without a library card.
If you want to check out materials (I do not) or use the public computers (I do), you will need a library card. This typically requires ID and an address.
Some things that can be problematic:
Libraries that are not genuinely public property.
I have been to a couple of branches (on in Oceanside) that was renting space in a shopping center. This is problematic in part because security is more likely to run you off while waiting for it to open.
We referred to one library as "(head librarian's name) Dungeon" because she was so awful. Her staff hated her too. We figured this out after she basically ran us off from her branch because it was just one branch of a system where the staff rotated around the system to other branches. Once staff in another branch figured out she hated us, they were even nicer to us, apparently to get her goat because she had far less power there than on her home turf.
Not near food.
Since we spend all day at the library doing freelance work and developing our projects, etc, we need to eat lunch and do snacks. A good library will be near eateries and shopping that work well for us.
If it is near food and has good outdoor spaces conducive to doing lunch conveniently, this is awesome. It is also nice if it is not overly far from a good camp site.