With that being said, NY + LA are my personal two favorite cities because these two cities combined cover such a large swath of the globe. No, the food is not as good as the country of origin, but it can get pretty close. And then you have such a variety. Just this past weekend (in LA) I had Jamaican food on Friday, Israeli food on Saturday, and Thai food on Sunday. And they were all pretty top notch.
I've heard Houston also has quite a diversity of food, I've heard Chicago is pretty good as well. To me, to be a best food city it is imperative to cover a broad section of different cuisines. By that metric, LA is world class and (for my taste and the kinds of food I like), unbeatable.
EDIT: One other thing I forgot to add. LA has a great spirit of innovation when it comes to food. You see people selling food out of their house, on the sidewalk, in parking lots just to get their idea out into the world without a lot of overhead. There's this feeling that if you try something new and capture people's attention you can make something big out of your food. And I think that's amazing (also it helps keep the costs relatively low for the consumer which is a bit of a bonus).