Choco Flan C.
Yelp
I love this market, mostly because my two favorite vendors provide almost more than I can carry home.
First of all, if you prefer organic foods, you can go to Peasant's Plot. They aren't certified organic yet, but they don't use pesticides and are a CSA. They're filled up for this year, but I intend to sign up next year. There are some things only CSA members get. For example, this morning I saw some truly marvelous gigantic garlic but they were CSA only. (sad face!) They have individual memberships and people who pick up their groceries on bikes, so if you are a single person, I would definitely consider them for membership.
If you like to cook with mushrooms, head on over to River Valley Kitchens. They have fresh Shitake, White, and other varieties. Even better, you can get frozen mushroom burgers (portabello and black beans), their stuffed ravioli (your choice of butternut squash, portabello or I think asparagus), a steak sauce (they are planning to rename it) that has portabello and wasabe that is great on just about anything, various small batch, freshly made granolas, and various salsa and pasta sauces, made in small batches with yum, portabello in it.
I've also picked up some gorgeous orchids, fresh herbs, and there is a knife sharpener there as well. I've not tried it, but Breadman is there as are some other baked goods vendors.
The Tuesday Morning Farmer's Market is sponsored by the City of Chicago, which usually promoted by the Alderman, and the Thursday Evening Farmer's Market is sponsored by the Chamber of Commerce. Not all the same vendors are there on both days of the week, but if mushrooms are your thing, then you are in luck on both days.