A Blog Supreme, the NPR jazz blog, has a jazz-oriented playlist for Independence Day,
Five Platters For Your Fourth Of July Picnic. I won't argue with any of them, but I will offer a few more suggestions.
X, "4th of July," from See How We Are (CD 23529)
Bruce Springsteen, "Independence Day," from The River (CD 5185-5186)
Violent Femmes, "American Music," from Add It Up: (1981-1993) (CD 7407)
Jimi Hendrix, "The Star-Spangled Banner," from Jimi Hendrix: Woodstock (CD 1745)