Cafe Mustache has free wi-fi that shuts off at 6pm every evening, as well as coffee drinks, sandwiches, vegan chili, and a bar that starts serving in the evening. Very close to the California blue line.
Order and pay at the counter. $10 credit card minimum. http://bonbonsandwiches.com/
Caveat emptor: the "vegan" Korean barbecue wings have a sauce that contains honey. As far as we know, other items marked vegan are truly vegan. If you want to be on the safe side, ask about honey in the items you order.
Their breakfast hash combinations are available in vegan-friendly versions (tofu and/or avocado replace eggs) and options are clearly marked. The also have coffee. The dining room is small and cozy.
This is a national chain (started in Colorado) but it has only a handful of locations nationwide, with several being here in Chicago.
All-vegan menu. Ordering is at counter before sitting down. They have a great beverage selection that includes a few bottled beers as well as house-made lavender lemonade and hot chai.
This place is a tiny storefront with three tables squished between a CVS and a Mediterranean restaurant. If you order over the phone instead of with GrubHub, delivery is pretty fast. Their veggie chick'n isn't vegan but the veggie fish is. I'm a fan of their vegan ceviche. They don't have a website, but they're on Yelp: http://www.yelp.com/biz/vegetarian-express-chicago