Go over to http://www.chicagokitesurfing.com
and check out the where to ride section. http://www.chicagokitesurfing.com/wheretoride/illinois.html
Closest north is Waukegan or Zion Illiniois beach state park on a N-NE-SE-S and Just a smidg SSW at Waukegan. South of Chicago your into Indiana at Wolf Lake, Casino or Lake/Miller. If you don't mind a bit of a drive north Sheboygan can sometimes get a nice thermal boost but that dosn't look like it's been going off this season. The east side of the lake over in Michigan is nice. Water's about 5 deg warmer most of the time. Finally got up to comfy without booties weather. Only place you have to have some kind of competency rating to kite is Chicago it self at Montrose. http://www.chicagokitesurfing.com/ridinglocations/rules/montrose.html
If your coming from NZ and you have some space in your bags could you bring some wind with you? Or perhaps some magical rocks that make wind when you shake them. Pack your big kite.