The Randolph Street Market Festival kicks off its summer season this weekend - Saturday 10-5 and Sunday 10-4. Part flea market/antiques fair, part indie designer mart, part food festival - it's like Portobello Market meets the Midwest. Admission is $10, and pets are allowed for the outdoor part of the Market. (Market rules state no Dobermans or pit bulls, however.)
The RSMF runs the last full weekend of the month from May through the end of September.