For nicer food, Watt's Grocery is right next door to Broadstreet and aims to be kid-friendly. I wandered in after a very sweaty, dirty afternoon of play, curious about take-out dinner options. Amy, the owner, was in the front of the restaurant and was VERY nice and welcoming, helping us find the best gluten-free options for DS on the menu. They have a nice book nook and really welcome children. I haven't tasted enough of their food to recommend much more than the kindly atmosphere!
We've also been to Blue Corn Cafe on 9th street, which has a very enticing dedicated kid section [with big TV and videos, natch, but my kids played without noticing it much]. The waitstaff was so nice and the food is yummy. I think there's a lot in Durham for kids and parents.
For quick, nutritious and not super expensive bites, nothing beats Whole Foods for us on Broad St. I love that we can get our food QUICKLY. The Durham WF has really expanded their take-out options and there is plenty to choose from.