What's with all the Gatlinburg bashing? I have fond memories visiting when I was 16, admittedly it was part of a high school trip so cuisine wasn't foremost among my concerns. I suppose if you want the experience of the Smoky Mountains with a little more culture, you can base yourself in Asheville...

As for Chicago, I think one of the main draws has to be architecture, there are quite a few interesting buildings in the city, and Frank Lloyd Wright is from Oak Park (a leafy suburb). As a major city, it also has a variety of museums. It's also somewhat of a hipster paradise, at least according to my hipster friends who moved there in droves after college. If you're interested in fancy food, Alinea is the best restaurant in the country (according to "The San Pellegrino World's 50 Best Restaurants" rating).

Re: The OP, I think the appeal of the US for the British is largely based on the familiar. The US and UK aren't exactly on opposite ends of the cultural spectrum, but there are many subtle (and a few not-so-subtle) differences between the two that make for a neat experience. And sure, you can find similar scenery (mountains, canyons) and experiences (museums, people) in other countries, but that could be said of any country, so I don't know if that's a reason to exclude the US from travel plans.