What you won't find in Britain is "good" Tex/Mex food, a.k.a. Mexican food. Tex/Mex consists primarily of tacos, burritos, enchiladas - that kind of stuff. While you may have Mexican restaurants in Britain, I assure you that none of them are good. The best Mexican food in the USA is found on the western half of the country, although there are some reasonable places in the east. What to order.....personally I'm a fan of enchiladas, those are my barometer for how good a place is.
BBQ is something you won't find in Britain. BBQ is a uniquely American creation. Best BBQ is found in the south east, Texas, St. Louis and Kansas City. I'd recommend a sampler with ribs, pulled pork and brisket.
Hamburgers are another thing we do well in the USA. Try finding a 5 Guys or an In/Out burger place. 5 Guys is a national chain. In/Out is primarily found in the west. Another possible burger place is called Red Robin. Red Robin can be hit or miss. The original Red Robin is in Seattle and was excellent, some of the franchises, in particular the ones in the east aren't as good. In NYC, try 5 Napkin Burger. Each town / region you go to will have it's own local best burger joint, without knowing exactly where you're going can't be more specific. What I've recommended are chain restaurants.
Ice Cream!!!! Depending on where you are the choices will be different, but find the best ice cream stand where ever you visit.
The other thing you can't get in Britain or anywhere in Europe is a proper mixed drink. Y'all just don't get it when it comes to making cocktails. When you go to a restaurant with a bar, order a mixed drink (rum and coke, vodka and tonic, gin and tonic.....whatever) so you see how they are supposed to be made.
Each city/town will have their own best restaurants. If you want specific recommendations you'd need to say what places your going. There is a smart phone/tablet/website called Yelp that is good for recommendations. There is also a website called chow.com that focuses on restaurant recommendations by city/region. Click on "chow hound discussions".