Answer:
Loyola, Northwestern, and University of Chicago are the only large academic libraries in Illinois that do not participate in I-Share. These libraries do offer visitor access. Hours and policies vary so be sure to inform yourself via the links shown below. Bear in mind, students may use the collections on site but may not borrow from these libraries directly.
Full-time faculty may participate in the OCLC Reciprocal Faculty Borrowing Program. This program enables full-time faculty to gain borrowing privileges and on-site access to the collections of these academic libraries (and many others across the country).