Video with scenes of Rush Street between Chestnut and Oak, 1966:
• Video Link
Between the righteous neighbor groups and former Alderman Burt "Sold!" Natarus, the entire area has been successfully condozed in the intervening decades. A couple old buildings survive near the intersection of Rush & Chicago, otherwise all that's left of the district is north of Oak Street, and of course those have been largely sanitized compared to what's shown above.
Be sure to check out flickr user davidwilson1949's sets as well. Here are some teasers.
Broadway north from Diversey, 1987 (everything on the left side is gone):
Halsted, looking south from Roosevelt, 1990:
Looking east along Superior, from Dearborn, 1967 (basically every foreground lowrise building is long gone:
NE corner of Chicago & State, 1967 (again, everything in the foreground is gone, replaced by a crappy McDonald's and bland Loyola University buildings):