I see that other posters have found Amarillo a challenge as well, and I thought I'd just share my experiences after being unexpectedly stuck there for a day in the middle of a trip.
Generally: From what I observed by driving around with a lot of time to kill, local specialties seem to include BBQ and catfish. A difficult challenge if you're a coffee snob--- I didn't see a single Starbucks and precious few non-chain places to get espresso or good coffee. Several potentially interesting eating places along SW 6th street west of Georgia, which seems to be an arty neighborhood. There doesn't seem to be much in the downtown business district.
First dinner: Celia's mexican, 6th street west of Georgia: I had a really quite good pork chop, my partner had a combination plate with tamale, taco and chile relleno. The style was unfamiliar to me--- mildly spiced and more tomato-based than, say, New Mexico or most other Tex-Mex I've had. Not sure if it was a local style or just that restaurant. The people were friendly.
Lunch: Ribs and More, 6th and Georgia. A small, friendly place with good beef BBQ and pecan and sweet potato pies that both looked and smelled amazing. I only tried the sweet potato pie.
Dinner again: Excellent takeout from Catfish Shack, SW 45th between Western and Teckla. A tiny little takeout place that somehow looked right. I got catfish, hush puppies and fried okra. Really good if that's the kind of un-fancy, non-health food you're looking for.
Breakfast: Donut Stop. They have pretty good donuts and, importantly, an espresso machine. They seem to be a local chain that has bought up pre-existing buildings, because each location looks different. They all seem to be very attractive 40's-50's-style buildings, though. Several are visible from I-40, including one at Bell.