Bulls games are a good time if they are in town. For sure. I completely agree with the first reply - The Green Mill is awesome. It used to be a speakeasy and Al Capone hangout. You can't get much better than that. Add the fact the music is always great and the martinis are the best. For Blues you have a couple of choices (And I agree, see some blues). I say stay away from the usual tourist joints and hit one of two places - Kingston Mines, or almost across the street - B.L.U.E.S. (Don't mistaken this one for Blue Chicago, the tourist blues bar). I prefer B.L.U.E.S. over Kingston Mines because it is small, intimate and dirty. Just like a blues joint should be. Though the women tend to gravitate towards the Mines. Both places are in Lincoln Park.
The Blue Note is also a great place over in Wicker Park. As is House of Blues downtown, depending on the act. Joe's on Weed Street is great for catching a sports game and has live music most nights. Tonic Room is another cool live music venue. I love Iggy's and then there's the famous Double Door. Though Kendall's in Lincoln Park will have the mid-week younger crowd for happy hours and the like.
The W Hotel bar on the Penthouse floor at W Lakeshore is great with awesome views and very attractive waitresses/patrons.