You might try Hassayampa Inn - a lovely old hotel with restaurant near Whiskey Row.
If you like traditional Italian food, Rosa's Pizzeria is wonderful! It is NOT just pizza. Everything we tried there was excellent! Arrive early, though. It is a popular place, and it is family-friendly.
I agree with Judith D. We stayed at the Hassayampa a few months ago, and the restaurant there was quite good, though the service was a bit slow. If you are not in a hurry, it is very nice.
We found the breakfast/brunch there to be especially good.
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