In the late 19th century, the American musical tradition was pretty much an extension of the European musical tradition, which is generally why American composers of that period aren't generally held in the highest regard; American concert music was still maturing, and the first real American musical forms -- rooted in the emergence of jazz -- had yet to fully emerge. But there was still good music being written, and it's really Eurocentrism that keeps a lot of it from being heard more.
A good example is this fine symphony by Amy Beach, who lived from 1867 to 1944. She was a prodigy and a gifted performer who received great acclaim as she took the stage in her late teens, but then she married a man who decided that she shouldn't perform much and that she shouldn't study composition with a teacher, so while she continued making music, I must inevitably wonder what art was stifled by our society's sexist idiocy of the day. During her lifetime, her compositions were actually credited to "Mrs. H.H.A. Beach." The mind, hopefully, reels.
Beach's Gaelic Symphony is reminiscent of Dvorak (who was a heavy influence upon her) in its orchestration, and she used a number of Irish songs in the symphony's melodic material, creating a work that is fascinating to hear. Beach wrote this symphony early in her musical life, before she embraced native musical material, but it is still a fine and invigorating listen. In her later life, Beach would live for 34 years as a widow, composing and teaching. She never wrote another symphony, unfortunately.
Here is the Gaelic Symphony by Amy Beach.