The New York Times will often feature opinions columns from conservative writers on staff, the most well known are David Brooks, Bret Stephens and Ross Douthat. With the ProQuest version of NYT access, you can search by the name of a writer to find their works.
Think tanks are "an institute, corporation, or group organized to study a particular subject (such as a policy issue or a scientific problem) and provide information, ideas, and advice." (Merriam-Webster)
Think tanks are typically NGOs and funded by individual donations or grants. They will usually publish articles, studies, or draft legislation relating to specific aspects of society or government policy. In the United States, there are a number of think tanks that are considered to have a conservative lean.
Descriptions of the listed organizations are from the Georgetown University Library libguide on Public Policy and licensed for reuse under Creative Commons Attribution NonCommercial 4.0 International License.