Right on the campus of the University of Chicago (and only about a block from Robie House) is the small, but very interesting Oriental Institute Museum, housing an excellent collection of ancient Near Eastern Art. It consists of only eight galleries, but the quality of items exhibited is very high. Most of the collection appears to come from the various archeological digs run by the University of Chicago in the early 20th century.
One of the most interesting of the galleries is the Egyptian gallery, which includes a giant 6-ton statute of King Tutankhamun, mummies, painted tomb walls, and variety of other Egyptian tools and artworks.