I leap frog around coffee shops pretty often. The library is always good, provided they're open. The Perfect Cup near the Damen Brown line stop is decent. I really like Red Eyes on Lincoln and Berteau.
My favorite neighborhood work place at the moment is Beans and Bagels on Montrose. Sometimes you need to fight for a table (depends upon time of day), but otherwise, it works out nicely. Prior to that, I was working out of the Starbucks on Wolcott and Montrose, too, which works but I'd rather support a local small business! :-) I've also hit The Perfect Cup a few times and would probably do so more often as it's a great place (just twice the distance of B & B for me). And I've found O'Shaughnessy's to be a great place for some leisurely work, too (the wifi is actually really good). Finally, I just recently hit the downstairs area at Mariano's, and if you can find a spot underneath/not facing the escalator, then I think that could work out VERY nicely.
Those are options for doing some work (business or personal) away from home. If you're looking more for coworking facilities, then I also would mention Platform. Great, cozy, efficient place in the awesome corridor. Last year they did offer a one week trial, which I used. Of course, you need to pay for it after that (and they offer multiple plans), but it's a really great local option (available 24/7)!
I hope that folks who "work" in these small or ... business BUY something! I have seen folks go in to these places get a small coffee or tea,,,, and sit there for hours while others look for a place to sit and enjoy their purchase ...