The Shedd Aquarium and the Field Musuem are great. The Art Institute is great if you wanna get your culture on... I think the Shedd Aquarium still has the Jellies on exhibit. You pay a little extra, but they are cool to see.
Boystown is great - always busy on the weekends. That's in the North part of the city. Not too far from Wrigleyville (weird how that worked out..) Just walk Halsted and you will figure it out. A lot of bars, usually pretty busy.
If you are not so much into the "gay scene", then I like to hit this bar on Hubbard called... (drum roll please) Mother Hubbard's. The rest of the bars on the street can be kinda douchy though. No worries however because Hubbard's, open til 4a, is one of the spots people hit up when the douchy joints close at 2a. You get the same crowd with less hassle...
Decent sports bar with decent bar food with a decent beer selection. As a bonus, I have never once been there and not been chatted up by the "straight" guys in the bar. A win-win in my book.
If none of that sounds interesting, just do what I do and start walking. You will eventually see something or run into someone that interests you and will pass the time.