I don't have any pictures of my own, and other than the Statue of Liberty, Ellis Island, and perhaps New York City, I can't think of any other decent symbols.
Since I was born an American citizen, I could never be sure on what exactly the American Dream is meant to be. The only thing I could deduce for the answer is to ask why everyone from around the world wanted to come here. To me, the answer is to escape. The popular topic today with immigration is mainly to escape poverty and violence, hearing about the cartel wars in various parts of Mexico, maybe other countries in turmoil. And this seems to have been repeated before. The massive numbers of immigrants from Europe and Asia during the turn of the 20th century, where you had revolutions and some cases of famine and unemployment. And during potentially violent regime changes in different countries around the world, you hear of refugees trying to reach other countries, USA included, even by illegal means.
I think the ultimate goal of the American Dream is freedom, whether from persecution, poverty, violence, slavery, and genocide, though it later shows not to be easily realized (we're not perfect by a long shot), and not everybody came here for that reason, like slaves taken from Africa to work the plantations.