Wicker Park/Bucktown have a lot going for them, but the big negative is that they've turned into Lincoln Park West in recent years - which means you tend to have lots of douchebros roaming around, drinking heavily, screaming, and puking on the sidewalk at night. The problem is most heavily concentrated on the commercial/bar strips of Milwaukee, North, and Damen. I'd wander around there on a Saturday night just to see what you're in for there.

I'd second the Andersonville idea. The area is a bit more suited to gay adults with kids - lots of other kids in the area, a bit more of a mature/family vibe but still with lots of cool restaurants, some gay bars, etc. so you don't feel like you're in the suburbs. The proximity to the lake is also great for kids, as you've got a wonderful place to play/hang out close by.

It's also rather easy to get to the Blue Line from there - you can just take the Foster bus straight to the station at Jefferson Park. It's not the fastest trip in the world, but it's certainly easy and cheap. Personally, I'd find proximity to the lake to be a more important feature in Chicago than proximity to the Blue Line, but obviously that's just me.