Of course we can’t cover them all but here is a list of some of the signification 1960s events.
1960s Events, International, National, NYC

Riots

Watts 1965

Chicago 1968

Detroit 1967

Harlem 1964 and 1968 Post MLK Assassination

Newark 1967

Reports

1968, the National Commission on Civil Disorder (known as the Kerner Commission)

Pentagon Papers 1967

Knapp Commission about the NYCPD in the 1960s (1972)

Events

Chicago Democratic National Convention Riots 1968

Tonkin Gulf Resolution 1964

Bay of Pigs Invasion 1961

Cuban Revolution 1959

Cuban Missile Crisis 1962

Apollo Man on the Moon 1969

Assassinations

John F. Kennedy 1963

Martin Luther King Jr 1968

Robert F. Kennedy 1968

Malcom X NYC 1965

NYC Events

Wall Street 1968 and Hard Hat Riots 1970

Kitty Genovese Murder… Fact and Fiction

1965 East Coast Blackout

CBS News Biggest NYC Events of the 1960s

The Beatles 1964

NYC World’s Fair 1964-65

Verrazano Bridge Opening 1964

Republican, John Lindsay, becomes Mayor 1966

Woodstock 1969

Women’s Movement Protests

Anti-Miss America Pageant 1968

NYC Radical Women (Redstockings) Abortion Rights Speakout 1969