i have not been to any of the restaurants on the Duquesne Heights end of Mt Washington for years, but unless things have changes, there is nothing particularly kid friendly up there. They all are for the higher end adult market.
As the for Carnegie Science Center, there is nowhere to eat nearby, kid friendly or not. Not too far away is Peppi’s on Western Avenue, which might be fun for a kid. (See http://www.pittsburghlive.com/x/pittsburghtrib/s_195051.html
I can’t say I know of anything on the way to the Airport except for the Sharp Edge Creekhouse, which, while its known for its Belgian beer, has a menu a kid could like.
I heartily endorse DeLuca’s, Klavon’s and either of the unrelated Original Hot Dog Shops (Oakland or Station Street.)
Let me know if you want more info on any of these options