Ah, you might want to start with Mark Twain's Innocents Abroad
. Twain is very accessible and his work is in the public domain. It's in most if not all public libraries or they can order it for you quickly. If you enjoy it, read his other stuff, too! Huckleberry Finn
is one of the great American novels.
If you're looking for a female writer, try Jane Austen. She wasn't a travel writer, but her works are, justifiably, classics. They are romances, often about manners and position as that was the world she knew. She died in 1817, so everything is very clean of course. Again, it's all in the public domain, and any library worth its salt will have Austen or a quick means of getting it into your hands.
And when you go to the public library (you should! Libraries are one of the backbones of our society), talk to the librarian and explain what you're looking for, and what you like to read.It is their job to know, so they can give you more contemporary recommendations.
In order to help with your cellphone addiction, you might want to make a rule with yourself that you either don't bring your phone inside or, at the very least, you don't turn it on, when you're at the library. Just, use that space to either interact with the people around you or to read. I think if you set aside spaces like this for yourself that are cellphone-free zones, I think you will start to find that the world does not end when you're not available 24/7.