There have been a lot of good suggestions on this thread, and I would second (or fifth) most of them: buffalo wings, fried chicken, mac & cheese, salad bar. All good suggestions. But, to be honest, I think the key to making a really good, authentic American restaurant is not just filling the menu with 'American foods,' but making sure that all the food is made in the right way.
For example, lots of places have 'American' pancakes, but they're never quite right. And I've never seen proper hashbrowns, just the frozen, pre-formed kind. Or take steaks, as an example. They're not exclusively American, by any means, but whenever I've had them in 'American' restaurants here, again, they're just not right. There's no seasoning, and they're rarely char-grilled, so they just don't taste the same. There are lots of other examples of things that I've ordered, and just been disappointed in, because they weren't what I was hoping for.
So, whenever you've settled on what you want on the menu, go to the states yourself and find out how they're supposed to taste. Then, ask yourself if it's possible to replicate that in the U.K.. Often, the answer will be yes. But sometimes it will be no, because the available ingredients just aren't the same. In that case, for the love of God, just don't try. Because there are tons of Midwestern staples that I miss dearly, but if I saw them on a menu here, I wouldn't dare order them for fear of how badly wrong they'd be.