When I think of American food I think of steak, fried chicken, corn on the cob, mashed potatoes, hot dogs, hamburgers, pot roast, chili, apple pie, Thanksgiving fare (turkey, dressing, sweet potatoes, etc.). For all I know most of these originated elsewhere, but they are what I think of when I think of traditional American Food.
To me a big thing would be to understand and develop a sense of pride in being American. I would do that by studying the American revolution. Not just the war, but the reasons behind the war. What was it that people were willing to die for? And then learn about how our country is different from others and what makes it special. This could extend all the way to things such as pride in out national flag, as mentioned by a previous poster. If you want to bring it into current events you could do a study on how our current government operates compared to how the founding fathers intended it to operate. (BTW - I am not saying it is being run correctly or incorrectly - just that it would be a good way to look at the current culture.)
If you are looking more towards exposing them to current pop culture, you need look no further than Disney. They seem to be involved in everything. I can't really make any recommendations though, as I spend my time trying to lessen my kids' exposure to it.