The National Motorcycle Museum in Anamosa, IA, has a fairly large collection of mostly turn-of-the-last-century bicycles: penny-farthings, "safety bicycles," etc. Kinda makes sense, since the earliest motorcycles were pretty much just motorized bicycles.
A personal favorite: a naphtha-fueled bicycle headlight.
In Cudahy, South Shore Cyclery has a collection of vintage bikes from all around the world. I saw a J. C. Higgins Flightliner middleweight like one a neighbor of mine in Beach Park had. See at www.southshorecyclery.com