The Ambassador Hotel would be a great affordable family option in Amarillo. We stayed a few months ago, and found the hotel to be very nice and classy. The hotel had a large indoor pool which was great for our kids. We were on a budget and liked that our room had a sleeper sofa for the kids to sleep on.
My mother and I drove cross country from Idaho to Florida last Summer, and our third night's stay was at the Motel 6 East I-40 in Amarillo. It's nothing really fancy, but the price for a night's stay is reasonable and there is a swimming pool. The service is great, and I have written a review on it on my journal "Driving in Cruise Control II". The hotel is located near many restaurants that you can dine in at or get delivery to the hotel.
Motel 6 E I-40
4301 East Interstate 40
Amarillo, TX 79104
www.motel6.com
Good luck!
Dianne