I was at Monk's a few weeks ago on a Saturday evening (6ish), and the table next to ours was a couple with 2 kids.
Didn't really bother me at all, though I think Monks is a lot more fun for a 30 year old than a 3 year old, but the place was busy enough and loud enough, that even if they were freaking out, it would be hard to hear them across the restaurant.

I think a little boy going to the corner bar with his dad has a cute novelty to it, as long as he can just sit down and shut up or play with a toy or something.

I can barely stand going to places like Continental, or virtually anywhere in Old City anyway, kids usually provide an interesting show in a conversational environment anyway.

I whole-heartedly agree with the Juice as far as exposure to the Public for kids - that's one of the great things about living in the city - the diversity of people (even far beyond ethnicity) does a lot to make anyone, let alone kids, think of people who are different from themselves. I grew up in the burbs with a bunch of Irish and Italian catholics, and it wasn't until 2nd or 3rd grade that it began to sink in that not everyone in my school wasn't catholic and lived in a house just like mine. Even though I visited my grandmom in South West Philly every weekend, I always kind of thought everyone in the Burbs was just like me.

The City life is great - on my walk home from work, I saw rich MILFs in Washington Square, a schizo at the SuperFresh, and an obese and likely diabetic black woman in a wheelchair screaming to a shop owner about how horrible Imus is for saying "Ho" versus rappers because she could "hear the hatred deep in his soul."

Cheers, kids!