In Chicago, Cermack, Pete's those mexican mart have chinese food too.
South Chinatown, Hong Kong mkt on 24th street, free parking.
华埠百家乐,晨星,永昌,Mayflower (五月花)all have good chinese food.
2 Hmart one in Naperville, the other in Nile, Wakegon.
a couple of taiwanese grocery stores, ex, one in international plaza, Hinsdale.