They just opened their new place at 937 N. Rush St.. They feature live music 7 nights a week. I posted a link to their Facebook page below which gives you all of their upcoming events.
Just across the border in Edgewater there is live music at Uncommon Ground where there is music almost every night. http://www.uncommonground.com/pages/calendar/52.php.
Evanston's Space, http://www.evanstonspace.com has nightly music and many discounts at http://www.goldstar.com/events/evanston-il/live-music-at-spa Don't miss the food at the Union Pizzeria (way more than pizza).
That should get you started.