Nixon was not a conservative.
You can read Nixon's remarks on the opening of the Woodrow Wilson Center for Scholars here:
Along with most Presidents of the past half century, I have long been a student of Woodrow Wilson.
Nixon's Quaker mother was a great admirer of Wilson, and he definitely tapped into that. Popular culture in the 40s was saturated with the idea that we could have avoided WWII if only we'd listened to Wilson, and Nixon, like many in his generation, picked up on that notion and clung to it.
A lot of Nixon's interest in foreign policy related to Wilsonian grand schemes for peace building. He wanted to build international institutions and some kind of system to ensure peace, and he saw Wilson as a precursor. Garry Wills's book on Nixon pursues the idea that Nixon was the last Wilsonian liberal.