Sunny Rock Cafe in Blowing Rock for breakfast. Can't beat the breakfast burrito.
Coyote Kitchen is awesome. Never would I have thought salmon and sweet potatoes would be so good together. Also, get sweet potato fries as an appetizer. I'm not sure what kind of crack they sprinkle on them, but its top shelf. I don't think you have little kids, but if so, they eat free too!
Casa Rustica is great too like
@StretchASU said.
The Cardinal has great burgers, but a bit pricy.
If you like deep dish pizza, Capones pizza is amazing. I'm a huge fan of deep dish, and don't really like tomato sauce, so their deep dish with Alfredo sauce is one of my favorite pizzas ever.
Black Cat Burrito is not what it used to be, but is still quite good.
My wife loves Storie Street grill in Blowing Rock and Our Daily Bread in Boone.
Of those, Coyote Kitchen is the most dog friendly (covered outside seating), and the Cardinal and Capones might also have outside seating.