Shop. That'll expose you to a huge amount of American life. Be sure to stop by different kinds of stores--convenience stores, grocery stores, supermarkets, gas stations, laundromats, restaurants, shoe stores, clothes stores, toy stores, electronics stores, car dealerships (if you dare...)... Be sure to go to places aimed at different social classes (both the dollar store, the Pottery Barn, and...whatever it is rich-ass people go to; the used car dealership, the Toyota dealership, and the place that makes custom cars). Also, ride some buses or other public transit if you want to see the racial and other demographic differences between the haves and have-nots of the nation.
If you plan to go to rural places, never travel alone. Good advice for anyone, moreso for someone foreign, especially if you have any trait that people could interpret as marking you foreign (like if you have an accent, speak in a foreign language, wear giant flag of Not America on your chest, etc.). There's a lot of ire aimed at foreigners, especially in the South, near the Mexican-U.S. border, although whites and English-speakers are safer than most. I speak not just as an American, but also as someone who's been mistaken for a foreigner because of a nearly imperceptible speech impediment that sounds like an accent. (Some douche in my speech class told me my political opinion--which differed from his--didn't matter because I wasn't American, anyway. What a cock.)