I spend a week in North Conway every August, here are a couple of places that you might like.
Horsefeathers has very good food, the burgers and sandwiches should run you less than $10. You can check the menu out here,
Horsefeathers Restaurant, Great dining at the landmark neighborhood eatery in North Conway, NH 03860
If you like Mexican, I had a very good meal at a place called North of the Border Cafe. The prices were very reasonable, you can check out the menu here.
NOTB.html
Delaney's and the Red Parka are also good, here are the links.
Delaney's Hole in the Wall - Homepage (http://www.delaneys.com/index.html - broken link)
RedParka