The majority of the hotels in Amarillo are near restaurants, so that should be no issue. There are also quite a few places that deliver, like Pacific Rim, Jason's Deli, Jimmy John's etc. So at least you wouldn't be confined to pizza if you want to stay in.
I would recommend you rent a car if you want to do shopping, eating, and the usual travel fun. The city is too large to walk, but our public transit is crap, and taxis are expensive.
Feel free to PM me with questions or recommendations on things to do