The modernist music of America shares a number of commonalities with that of Europe: it is somewhat more chaotic and less formal, it uses some non-musical textures, and it integrates popular music to a large extent. George Gershwin is a very good exemplar of this style. He began his career as a composer with jazz music that was not intended for a concert hall; he turned to a more classical style after a trip to Europe in the 1920s, during which he composed his most famous work, Rhapsody in Blue, and the symphonic poem An American in Paris (1928). Here is a recording of the latter:
The piece is programmatic: it begins with a sudden, loud series of themes which are supposed to represent the overwhelming impression of Paris. The jazz influence and lightheartedness of the music are immediately evident. Around 7:30, the music changes to a bluesy rhythm and a blues scale as the subject thinks of home. Like the other Modernist composers we've mentioned, Gershwin takes a lot of liberties with tonality; however, unlike Schoenberg, he doesn't create a deliberately obscure style, but rather fuses preexisting styles in an accessible way.
Aaron Copland was a later composer and more strictly classical than Gershwin. His style is strongly influenced by folk music and, like Gershwin, he consciously worked to ensure that it had wide appeal. His most famous piece is the ballet Appalachian Spring, now usually performed as an orchestral piece. Despite the name (in which "spring" refers to the geological feature), it was intended to depict pioneers in Pennsylvania. Here is a recording:
The piece is generally tranquil and pastoral. It is characteristic of Copland in that it mixes tonal classical music, some atonal diatonic influences, and folk melodies (like "Simple Gifts" at the end). If you are reading the score, it is superficially rather similar to Schoenberg or late Stravinsky; Copland, though, managed to find a way to use atonal, polyrhythmic techniques to achieve bright and tranquil sounds.