There is a museum across the road on what was called Mainside when I was there. I do not know how hard it would be to get on base to see the museum.
Here is the web site: http://www.history.navy.mil/museums/greatlakes/index.htm
RTC is a military base...the only shop is the NEX on base that your sailor can take you to at PIR (and is PACKED after PIR) and as far as I know there is no museum....the big NEX is north of the base
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Here is the web site: http://www.history.navy.mil/museums/greatlakes/index.htm
Yes, there is a museum on the base. It's called the Great Lakes Naval Museum.
http://www.history.navy.mil/museums/greatlakes/index.htm