I regularly go to these Columbus area libraries to use the computers.
Massive multi-floor library has plenty of computers for public use. Library serves as host for special events, from job fairs, author's lectures, to weddings.
Main Library, Columbus Metropolitan Library
Peaceful library to go to. I enjoy going into the computer lab to use the internet. I like that the library has vendor machines for sodas and snacks.
Old Worthington Library
Currently open during renovations. Located just outside of Columbus. Nice library to spend the day in. Comfortable areas for computer use and reading.