I would actually say that it's the other way around, being that the Italian culture is much older. For example, look at the architecture in the U.S., especially the government buildings, which are Roman-inspired. Pizza, on the other hand, is a blend, since it was invented by an Italian-American in New York (though the Italians claim that they just made it better). As far as pop culture us concerned, one is not keeping up with the Joneses/Kardashians if one doesn't own anything by Gucci, Armani, or Prada. The one thing that Americans did adopt was organized crime, best portrayed by The Godfather and The Sopranos. But I wouldn't go as far to say that that has become part of American culture. California has successfully adopted the Italian way of wine-making, even outperforming Italian wines in world tasting championships.
Italians are proud to be Italian, and have adopted very few American cultural ideals. Probably the biggest American ideal is the freedom that women have in Italy, though the mentality is still very old-fashioned and provential in small towns, especially in the South. Legally, women have the right to vote, work and earn equal pay as men, and choose whom to marry (or not), and live alone, buy and sell property, and so on. There are quite a few women represented in Parliament, as well as in local politics - something the U.S. can learn from the Italians!
There are many differences and similarities in relation to American and Italian cultures. Looking for similarities between the two nations on a cultural level, we will be addressing some generalities but these might be telling examples of how we share certain perspectives and values.
Here, I will offer a few ideas that you might investigate further in your research on this topic.
The first similarity that comes to mind is a focus on the culinary arts. While America has not historically been a nation concerned with the arts of cooking and baking and the like, the United States is experiencing a significant upswing in a popular interest in high-end cuisine. Italy has long been a "food nation," exporting its tastes and expressing pride in its food culture.
A love of sports is also characteristic of Italian and American cultures. While Italians and Americans each champion different kinds of car racing, each country has a vibrant interest in racing. Perhaps more popular though is a love of professional basketball shared in both countries. Looking past specific sports, we can point to a robust interest in watching and talking about sports (as well as donning sports paraphernalia, especially jerseys) across these cultures.
Although fashion is arguably a more central aspect of Italian culture than it is in American culture, there is certainly a popular fascination with this industry in both countries. Fashion and a certain sense of "class culture" are linked in America as they are in Italy, yet fashion also offers a way for the average person to approximate status via a carefully curated wardrobe. Culturally, this trend is not about "looking good," it would seem, in either country. Rather, the fixation on fashion is about expressing a knowledge of the latest ideas in clothing and apparel.
When it comes to world fashion capitals, Milan, New York and Los Angeles are at the top of the list.
Finally, we might look at the ways that both American and Italian cultures present a divide between urban and non-urban sensibilities. Each nation boasts a number of sophisticated and urbane sub-cultures focused in its some of its cities (New York, San Francisco, Los Angeles, Rome, Milan, etc.). The Italian countryside is probably more romanticized that its counterpart in the United States, but the sub-urban life of America is an integral element of American culture just as non-urban life in Italy is characteristic of Italian culture along with its city life.