(I am making a judgement call based on your pictures and profile in regards to the bars which I think you will prefer.)
How many nights will you be here? This is what I am thinking for a Saturday night.
Start at Roscoes, then to Sidetrack, end at Hydrate or Charlies (both of which close at 5am.
SPIN has come into its own in the past year or so also.
As for straight bars I cannot give a professional opinion, but BERLIN is a great mixed crowd. Great music, everyone dancing. Downfall is that there is one bathroom in the whole place.
Having said all this if you are looking for "fun" afterwards there is Steamworks which will be plenty busy on the weekend. If you want seedy and not pay to enter a bathhouse there is a bar far north called Jackhammer. The upstairs is nice, but they have a basement (on the weekends) you must wear leather or just your underwear. This is farther north and if you are staying in Lincoln Park it would not be worth the taxi.