Peter Feaver at Shadow Government ("Notes From The Loyal Opposition") thinks about grand strategy (so you don't have to).
Many critics claim that the United States is simply too disorganized to do strategy on a grand scale.
This gets to the heart of why you get the odd argument that we had a grand strategy during the Cold War but we haven't since. When critics say that we haven't had a grand strategy since the end of the Cold War, what they really mean is that we haven't had a label like "containment" that enjoys widespread popularity. This is true, but trivial.
In fact, since the fall of the Soviet Union a 5-pillar grand strategy has been clearly discernible:
Pillar I. The velvet covered iron fist. Iron fist: build a military stronger than what is needed for near-term threats to dissuade a would-be hostile rival from achieving peer status. Velvet covered: accommodate major powers on issues, giving them a larger stake in the international distribution of goodies than their military strength would command to dissuade a near-peer from starting a hostile rivalry.
Pillar 2. Make the world more like us politically by promoting the spread of democracy.
Pillar 3. Make the world more like us economically by promoting the spread of markets and globalization.
Pillar 4. Focus on WMD proliferation to rogue states as the top tier national security threat.
Pillar 5 (added by George W. Bush). Focus on terrorist networks of global reach inspired by militant Islamist ideologies as another top tier national security threat, i.e. co-equal with WMD in the hands of rogue states. The nexus of 4 & 5 is the ne plus ultra threat.
No administration described the strategy in exactly these terms. Every single president succumbed to the political temptation to product differentiate and especially to describe one's own actions as a bold new departure from the "failed" efforts of his predecessor. Yet a fair-minded reading of the core governmental white papers on strategy, especially the National Security Strategy reports prepared by each administration, as well as the central policy efforts each administration pursued, reveals a broad 20-year pattern of continuity.
All post-Cold War presidents championed the first 4 pillars. The last two presidents (Bush and Obama) adopted the last 2. And the major grand strategic moves of the period derive from one or more of these pillars: eg. The outreach to India derives from Pillar 1, the invasion of Iraq derives from Pillars 4 and 5, and so on.
It may be easier to describe the grand strategy when there is an overarching existential threat to concentrate the mind. But as the post-Cold War has shown, it is possible to have a coherent grand strategy even when the threats are dispersed and less-than-existential.
The Cold War was not a time when everything was simple or when everyone knew priorities or everyone agreed on the threat. And it sure wasn't "a time of great stability and security unlike these really dangerous times today," -- a curious view that I hear most often from students who never lived through the Cold War era.
But it was a time when the much more obvious, and by the late 1950's possibly existential threat posed by the nuclear confrontation overlaid on top of a global ideological contest with the Soviet Union circumscribed strategic thinking in a way that is not the case today.