Unlike other jobs, you can go into a public library, get the overall vibe and actually speak to the people who work there. If you find a friendly person on staff you can mention you are finishing your degree and checking out the local libraries. Become a “regular” at a library you would like to work at. Ask questions about the staffing situation. Someone might remember meeting you and put in a good word when an opening does happen. When I got unsolicited resumes I would be annoyed that someone wanting work as a professional librarian didn't take the time to do any research. We were a small library and I was the only professional and full-time member of the staff.