Monk's Pub is a funky place, but their hours may not match yours. Lake & Wells
I love the Monk's recommendation. Used to go there when I worked at City Hall and had my farewell party there. Floor full of peanut shells. Dim lighting. Old school.
Miller's is another old school recommendation. S'posed to have good ribs but I don't recall if I've ever had them. I probably have.
With kids in tow, I'd check out the Goose Island Clybourn location. They usually have several somethings on tap you can't get elsewhere. The food is decent, too.
Even though Jeff thinks the Hopleaf is so far north, it's in my neck of the way (or nape of the woods, if you prefer). Kids are not welcome there, but that stretch of Clark Street has a lot of good bars and restaurants and boutique shopping. Half Acre and Metropolitan Brewing are close by (walking distance) as is Koval Distillery in the event you would have time for a tour. Hamburger Mary's brews their own beer, though I've found it to be hit or miss. They usually have a few on tap and it is actually brewed right there.
If you get up that way, I'd hit Lady Gregory's (good beer list, specatacular whiskey selection) and Jerry's, for sure. Big Jones is a New Orleans style restaurant and has a solid bar as well.
With the kids, you could hit George's for ice cream or Taste of Heaven (though they don't really like kids there).
Unfortunately, there's not that much downtown. You really need to get out into the funkier neighborhoods to find the gems.