The Stonewall Riots, the moon landing, Manson murders, Gadhafi rose to power and Woodstock all happened in the one summer amongst other things. Is there a particular reason why so much happened during this time period?
I suppose the first point would be to look at the counter factual: Did more notable events happen during the time period you mention than we would otherwise expect given a reasonable year to year variation? That is to say, if you allow for a certain 'randomness' and variation from year to year, we would naturally expect to see some years to contain a greater number of notable events, and some years less. Even so, take a look at the wikipedia entries for June - August 1968 and 1970:
https://en.wikipedia.org/wiki/1968
https://en.wikipedia.org/wiki/1970
Next we might ask: How significant or notable were these events in the context of the time? Certainly the moon landing was an event noted worldwide that was a watershed moment for popular consciousness regarding space travel and to a lesser extent the cold war. However, putting that aside for now, we can largely compare them to similar events that occurred in the previous or following summer. Who is to say Gadhafi's rise to power in Libya was more notable that Hussein's in Iraq, or the invasion of Czechoslovakia? Why should we consider Woodstock more notable than the Isle of Wight festival? Clearly civil rights and anti-war protests were common throughout the period, not simply in 1969. The French hydrogen bomb over Fangataufa changed the politics of the Pacific, culminating in such events as the New Zealand Navy sending two frigates in protest, the bombing of the Rainbow Warrior, the declaration of a Nuclear Free South Pacific, which substantially realigned politics across the region, and indeed the politics of Nuclear Weapons [1].
Next, I would note that the notability or significance of 1969 is at least partially due to a mythologisation of that time period, particularly in the USA. Complex social movements like the interrelated Anti-War, Civil Rights and Hippy movements are difficult to understand or even parse in their entirety. We have a tendency to focus on key events, which act as stand-ins for the entire phenomena. The "I have a dream..." speech has become in retrospect a focal point for the decades long Civil Rights Movement. The image of the Grande Armée withering away in the Russian winter has become the focus of the entire Napoleonic Era. The large social changes that occurred in the USA and elsewhere during the post war era that are often condensed into a sort of shorthand byword: 'The Sixties'. In turn, this is often further condensed into simply 'The Woodstock Generation' or 'the summer of '69'.
Woodstock was likely a significant event to those who attended. But its enduring fame can be more easily ascribed to the sensational images of the artists, crowds, and traffic jams which made, and continue to make, great media. The images of Apollo 11 taking off, or Neil Armstrong stepping out onto the lunar surface, even more so. Critically, by 1969, television was now nearly ubiquitous in the American household. Further, from its introduction in 1953 colour TV was beginning to take off. These technologies allowed the spectacle of these events to be captured and broadcast to a larger audience than ever before. What's more, high quality film and other images from these events survives to this day, allowing them to live on in the popular imagination in ways that events where television cameras were unavailable or even prohibited access such as the contemporaneous bombing of Laos, which remains the most heavily bombed country ever. With some 37% of the country still uninhabitable due to unexploded ordinance, people in Laos would undoubtably consider this event to be the more noteworthy.
In the end, no agreed upon definition of 'noteworthy' or 'significant' exists, nor can exist. History is the result of uncountable significant interrelated events. In the face of this immense complexity, we can only choose a few key phenomena, which we hope might serve as a lens through which to understand the wider context of that time. 1969 stands out in part because of media availability, and in part because the events you mention have been used by the generations since to mythologise that particular period of American history.
[1] Clements, Kevin P. (1988) Back from the brink : the creation of a nuclear-free New Zealand. Wellington NZ: Allen & Unwin.
