I just started working for the company that did the MHE system in that FC. My manager is telling me that I'll be at that site next week.
Markham is not exciting and neither is Harvey that's just to the east of it. You'll probably stay at one of the hotels off Halsted in Homewood. Make sure to choose the Ipass toll transponder option in your rental car as the site is right next to the tolled I294. Another option is to bring your own EZ Pass if you have it.
Directly south of the site, along Dixie Highway is Homewood which has a decent downtown area with some restaurants and shops. South of Homewood is Flossmoor which has an awesome brewery located inside of it's Metra Station.
Further West of your site, along 159th street is Tinley Park and Orland Park which have malls and many restaurants.