Fred's, Amsterdam at 83rd. Very kid friendly (heavy-duty dog theme, pictures of dogs everywhere, etc.) Good home-style comfort food (burgers, salads, mac-and-cheese), kid's menu, unrushed, fireplace in winter -- and a full, and very good, bar. http://www.fredsnyc.com/ For early dinner, check the "twilight menu".
Also French Roast, Broadway and 85th, though it can get frenetic sometimes. http://frenchroastny.com/
Around the corner (85th east of Broadway) is Dean's Pizzeria. Again, very family friendly, great brick oven pizza, perfectly serviceable pastas and salads, good bar. http://www.deansnyc.com/
2340 Broadway, New York, NY 10024
Five Napkin Burger on Bway at 84th. Good stuff, love their house made pickles.
I have not been but there is also Dean's on 85th, near Bway.
If you're going over to Amsterdam, I'd recommend B. Cafe.
215 W 85th St, New York, NY 10024
566 Amsterdam Ave, New York, NY 10024
Five Napkin Burger
2315 Broadway, New York, NY 10024