Most Influential American Musician of All Time?

can't argue too much with Satchmo or Miles
a few others to consider

Duke Ellington
Jaco Pastorius
Charles Mingus
John Coltrane

Leonard Bernstein in classical music. He was a

Conductor
Composer
Musician
Teacher and a very public advocate of classical music written in America.

In jazz I'd have to agree with other's nomination of Johnson, Armstrong and Ellington for their roles in contributing so much.

But if I can only nominate one who's music is still popular and regularily played it would have to be Bernstein. I don't listen to the fathers of jazz very often anymore important as their contributions may have been.

I would name Duke Ellington, Sinatra, Miles Davis, Bill Evans and John Coltrane. For the more recent major influences in jazz, I would say Michael Brecker.

There are probably different ones for different genres.
Armstrong, Presley, Dylan all deserve the nominations. One not mentioned so far is Gershwin. A man who conquered Broadway, Hollywood, and the Concert Hall. Left us memorable music and was adept at what he did.

Woody Guthrie the song writer.