Atlanta CH i/s/o Peninsula Hotel area child friendly truly local spots
Giordano's Pizza is half a block--very deep or stuffed pizza that you eat with a fork and knife. With child (or not) you can order ahead, ask the concierge to help and then you don't have to wait the 35 minutes for your pizza to bake.
Devon's Seafood Grill is about a block. This is actually a beta test restaurant owned by Houlihans. I think they may have opened a couple now, but I really like it--casual and reasonable seafooder.
Othewise, kids are welcome at most of the non-fine dining restaurants.
Knowing his or her age(s) might help in making recommendations. You might want to try the afternoon tea at the Penninsula, which welcomes children (and I believe has special selections just for kids). In terms of local places, the Pancake House (not related to any national chain) on Bellevue is good for breakfast; Oak Tree in the 900 N. Michigan building has a wide menu that's good for kids too (best for breakfast or lunch); you of course have the nearby original famous pizza places in Uno's and Due's; there are really tons of other restaurants in the area, and as the prior poster stated, most should be kid-friendly other than the fine-dining places.
re: juan epstein
Two points of clarification.
1) Uno's and Due's while good, usually have long lines and in my opinion are not worth more than a 15 minute wait. If you're over there, a few more blocks to Lou Malnati's on Wells and Hubbard is my personal favorite.
2) Original Pancake House on Bellevue is a chain, but still one of my favorite place for a short-stack and baked omelette.
OK, I lied, now a third point, it's cheesy (literally) but fun for a child who is at least 5. Ed Debevics on W Ontario at Wells is a burger joint that's actually pretty good. In the style of 50's diner with sassy servers it's touristy, but kids usually love it. And the burger is very good. Sometimes they even sing and dance.