Always call ahead to make sure the sources you need will be available on the day of your visit.
Many public libraries have local and regional collections and books and manuscripts. Start with the reference librarian and ask about collections which pertain to your topic. Ask for referrals to other institutions or repositories in the region which may have additional material.
Local colleges and universities may have manuscripts and archives devoted to local topics. Librarians at these institutions should be able to suggest other local resources.
Local historical and genealogical societies sometimes have their own collections. Contact them directly to find out about access policies (non-members may be charged a fee for access) and potential sources. Staff at these facilities may be able to suggest private collections among their members which may have useful material.
Family papers are sometimes retained by a family member, rather than deposited with a local library or archive. Local libraries and historical societies can be helpful in identifying these collections and putting researchers in touch with the appropriate contact person. It's best to arrange for access for such collections well in advance to ensure access during your visit.