I emailed my brother & his wife & son to ask because I couldn’t remember the names of the places we’d been, and they live there. I’m going to synopsize the responses for you. Well, my sister-in-law already posted, so just doing my brother & my nephew here.
Breakfast – Young’s. A downtown resturant/diner. Nothing fancy but a good traditional breakfast. My parents love it and take my brother there at least once per visit. My nephew loves the blueberry pancakes.
Breakfast/Lunch – The Bagelry. If you’re into "all things bagel and all that can be done with them". I remember I like this place. Good bagel sandwiches. Decent variety.
Lunch – Pauly’s Pockets. Affectionately known as "the falafel hut" mid-eastern/greek sandwiches and take out.
Dinner – The Three Chiminey’s Inn (www.threechimneysinn.com). Upscale, good food. My brother says his favorite meal is the Jefferson chicken. My nephew mentioned that Johnny Depp ate there recently. ; )
[My brother also said that most people in Durham eat at …Portsmouth. Next biggest town around. About 15-20 minutes away as I recall. There’s some Yummy food in Portsmouth!]
I hope this helps.