Derek Attig has a very pleasant summary of the book-browsing possibilities in my old stomping grounds at the University of Illinois at Urbana-Champaign. The university itself is the dividing line between the two cities. I suppose, depending on which side of the line you live, you’d call the area “Urbana-Champaign” or “Champaign-Urbana”; people call it either one, but the official name for the place is “Urbana-Champaign,” and that’s what I called it for seven years, from 1984-1991, when I was a student there, even though I lived in Champaign.
Attig is correct about the difficulty of getting into the stacks, but the undergrad library is easy to get into and has many comfortable spots to settle into and read. The various departmental libraries, scattered across campus, might also be easier of access these days, if you know someone, or if you are willing to write a letter asking for permission to visit.
The letter of request or permission is a good idea no matter what your purpose might be in visiting any university library. Illinois, for instance, has a fabulous collection in Renaissance and Seventeenth-Century literature (especially Milton), and solid collections in twentieth-century British and American literature. If there’s something you wish to see or some collection you wish to use in your research, write the library and explain your purpose. Chances are, they’d be happy to grant your request.
There are two other bookish places on campus worth visiting: one is a book collection hidden in the basement of a Catholic rectory across the street from the English building on South Sixth Street. You can go over there and have a sandwich for lunch and then browse the (mostly-used) classic book collection. The other place is the Reading Room of the Illini Union, just off the Quadrangle on campus. The room is spacious, well-appointed with comfortable, leather chairs, and quiet: perfect conditions for reading in the evening or on a rainy afternoon when the only proper thing a man or woman ought to do is curl up with a good book.