Hello Lance,
When in Chicago you must visit The Art Institute of Chicago Museum located downtown near the loop (the 'loop' is the downtown business area called so account the area is encompassed by elevated subway/light rail tracks). Their website is:
www.artic.edu/ where you will find all pertinent information, as well as examples of their permanent displays. One of the permanent displays (located in basement of building) is 'The Harding Collection of Arms & Armour' which consists of mostly european objects from the 15th - 19th C. According to website they have 225 objects from this collection on permanent display (I think the overall collection is around 1500 items). It has been years since I visited the Museum, but I remember the Arms display was impressive and I would certainly like to visit it again. Also, since the Art Institute is also a school, they have an extensive research library - 'The Ryerson & Burnham Library' - if you are interested. I haven't been there, nor searched their catalogue for ARMA related material, but I do know that they have a copy of Bengt Thordeman's "Armour from the Battle of Wisby, 1361" for instance. Access to this library is governed by a matrix of rules/hours (see website), but I believe that as a non-resident of northern Illinois (and if you show up when the stars are in proper alignment!) you would be allowed in if you'd like. I cannot commit to 'tour guiding', but if you're going to visit Museum at a known date/time send me a private message & I'll let you know if I can drive in & join you there.
Chris