I'm going to appear like a complete hair splitting nit picker here.
The pertinent question is "Conservative of what [values, traditions, policies etc]?"
Back in the Gorbachev era, the BBC used to talk about "conservative members of the Soviet communist party".
In American terms there are at least two political meanings of "conservative"
There is the "old" conservative, characterised in the 20th century by support for free trade overseas and laissezfaire economics at home minimal government, and privacy self reliant responsibility for the individual. They were against entanglement in foreign politics alliances and foreign wars, and against the Hoover and FDR New Deals at home.
To characterise what they were "conservative of" It would probably be the laissez faire classical liberalism of the Jeffersonians (jeffersonians tended to be far more consistent than flippy floppy TJ was himself).
Then there are the almost polar opposite Neo-Cons
I suppose type examples of the neocons would be William F Buckley and his circle of fellow active and former CIA agents at National Review.
Buckley had been a follower of American individualist anarchist, Frank Chodorov, but soon reversed his beliefs, coming to believe instead . that laissez faire should be abandoned for the duration of the Cold War.
Buckley's circle included former Trotskyite senior editor James Burnham, and former high ranking American communist party member and senior editor Frank S Meyer (both fellow CIA agents).
Then there are people like William and Irving Kristol and Robert Kagan. I still couldn't tell you what parts of the philosophy of Leo Strauss found their way in there or why.
To summarise (or perhaps to caricature) the neocon beliefs;
There is a highly millenarian (actually post millenialist) belief in American (and in a looser sense trans atlantic) exceptionalism and destiny to police and lead the world (so much for the ideas of avoiding entangling foreign alliances).
This really comes out in Bush the dumber's and Cheney’s speechificating after 9/11, complete with talk of America's destiny to do god's will (apparently Bush dumber and Cheney know what that is!).
War is seen as virtuous, and necessary to bring out that exceptionalism, both in individuals and in the chosen nation.
Government, instead of minimal in the palaeo-con vision, needs to be big authoritarian and intrusive (Patriot act, militarised cops and NSA snooping are examples of this - Remember that Buckley, Burnham and Meyer had worked for the CIA )
What are the neo-cons conservative of?
It would seem to be the pre fascist war mongering and big intrusive government of the "progressive era"; of Teddy Roosevelt, Woodrow Wilson and FDR, along with the extreme cronyism of that period too.
Buckley and his circle sought to purge the conservative movement of the small government anti war, "old right". People like John T Flynn and Ayn Rand, and groups such as the John Birch Society.