I'm a big fan of The Grind - but mostly for the free WIFI, friendly atmosphere and the great cupcakes (from Southport Bakery - best cupcakes period - not just in Chicago, best I've ever had anywhere, homemade included)
Intelligentsia while being possibly Chicago's best café for coffee drinks (and does have a great, if pricy, selection of sweets) is neither great for food or free wifi (no wifi at either location).
A recent favorite is Café Mud in Evanston (just west of the Foster purple line stop). Large, spacious room, free wifi, and if you ask they'll customize their sandwiches (I like asking for horseradish on the roast beef - pretty tasty, freshly made sandwich for a café).
Westgate on Madison in the West Loop is another good option for free wifi with okay food (nothing special but they do have a reasonably good selection of food options).
Argo Tea on Armitage and Sheffield has very good tea and coffee, free wifi, and quite tasty food options (best for the sweets). A little pricy and the space is tight - if well supplied with power outlets and a strong wifi signal.
Panera Bread, including the location on Diversey just east of Clark, is a good option for free wifi and decent if not great food (bread bowl soups can be tasty and the sweets too tempting...). Good to see a major chain strongly supporting free wifi as a competitive advantage. Though I do tend towards independent cafes, they are a good backup option at times.
Sweet Occasions (?) is a newer place just south of Clark on Sheffield. They serve Homer's Ice cream, make a great espresso, haven't tried their food yet but it is a nice, if smaller, space, across from the park and they have free WIFI - worth checking out and exploring further.
Art Gallery Café is a newer space on Division near Wood. It is an entire large storefront, next door to a good bakery - you buy your food and drink in the bakery and then go next door. Free WIFI though I've had problems with the signal not working in the past - lots of power outlets and a great physical space (two rooms, don't miss the back room which is thankfully where the smokers are leaving the large front room for the non-smokers.
On Grand near Ogden is Sip - which while small currently is in the midst of a VERY large expansion which will add space for approx. 100 people (I think - they are expanding back by building a very large expansion, including a new courtyard space, a lofted seating area and more - once complete they will be one of the cities largest cafes - and last I heard they plan on remaining mostly drinks and sweets - meaning you can walk down the street to Bari foods and get a sandwich to go - if it were just slightly easier for me to get to I could see it becoming my favorite café very quickly.
Hope this helps - lots of other great options in the Chicagoland area, thankfully many independent cafes seem to be opening and many seem to be surviving even in the face of Starbucks. I think Intelligentsia does Chicagoland a big favor by providing high quality coffee to a majority of the independent cafes around town - giving many of them a good step forward in providing a decent coffee (still need to prepare it well but starting with good beans definitely shows).
Shannon