I think the 1960s were definitely a net positive for America and Americans. Civil rights and women's rights were unequivocal triumphs, as was the newly heightened awareness of what we then called "ecology." The greater tolerance for different kinds of people and for weirdness were excellent changes. Pop music had its awesome big-bang moment, as you say, and movies and visual art were transformed in interesting ways, and we middle-aged people now get to wear blue jeans and sneakers and go to rock concerts and generally behave as if we're young until we die.
But we threw some baby out with the bath water. The mistrust of government that blossomed in the late '60s has become a chronic and in some ways pathological condition. We got carried away with the idea of victimhood, so that now white people and Christians and Wall Street guys cast themselves categorically as victims of bigotry. The latent American tendency toward self-righteousness and apocalyptic thinking got ratcheted up. The idea of one's "own truth" started propagating, and that solipsism is now pandemic.
And as I recently argued in a Times op-ed which bugged a lot of of '60s-romanticizers on the left and libertarians on the right, I think the "if it feels good do it"/"do your own thing" paradigm of the 1960s also helped enable the greed-is-good hypercapitalism and general selfishness that grew and grew afterward.