Parker and Otis is the default place I take out-of-towners for their first Durham lunch (... or Toast, depending on the out-of-towner). They have a long sandwich menu, so everyone is guaranteed to find something they like, and there's an amazingly curated, almost overwhelming amount of kitchen/cellar/pantry/lifestyle stuff to look at (and probably buy) while you wait for your food.
It's like... what a Cracker Barrel would be like, if it was cool and local and served mostly sandwiches.
They also have a few generous breakfast options that I've enjoyed on several (weekend) occasions, as well as a perfectly-sized little coffee bar/pastry corner, and a huge covered outdoor seating space.
I went for lunch today with coworkers and decided to go all in with the #29 - a peanut butter, bacon, and banana panini with honey on wheat (oh - and fruit on the side, to somehow "lighten it up" a bit). It was decadent, messy, and is now sending me into a mid-afternoon food coma, but totally worth it.