Can you just get the information you need at your local public library?

Yes and no - it will really depend on the topic you are trying to research and the type of sources that you need.

Public libraries are responsible for collecting sources that will answer the needs of all levels of community members, from elementary school children to teens to adults.  Public libraries tend to collect popular materials that appeal to a wide variety of users.  You may find that for some topics your local public library will be able to provide the information that you need.
  
Academic libraries are responsible for collecting sources that will answer the needs of their students, faculty, and staff.  Academic libraries tend to focus on scholarly materials intended for a more select audience. You will find that the library staff may already be familiar with your topics and research assignments.
  
Both academic and public libraries will do their best to completely answer your question in a professional, courteous manner.