depends what one is after.
to sample local creole, visit what's left of historic maxwell street market - Sundays 7am-3pm. i've bought back things that were stolen from my car - twice. it's fantastic.
to sample trendy hipster boutiques and such, look no further than wicker park - at 6 corners - intersection north milwaukee & damen avenues.
for standard luxury brand fare, Chicago's omotesando is downtown's mag mile & gold coast, most shopping delineated by rush st, Michigan ave N/S & Chicago, Division streets E/W.
This tip has the address "640 W. Roosevelt Road, 1600 N Milwaukee, 600 N Michigan"