Founded in 1977, the Cato Institute is a 501(c)(3) nonprofit research and education foundation in Washington, DC, generally associated with libertarianism, and the "principles of limited government, free markets, individual liberty, and peace" It avoids the term conservative.
Its webpage goes to some extent in discussing how to label it. Its emphasis is free-market capitalism — the most progressive, dynamic, and ever-changing system, which, it says, is called conservative — suggesting an unwillingness to change — only in the United States. Cato is opposed to social conservatives that favor state interventions in private life. Additionally, many contemporary American conservatives favor state intervention in some areas, most notably in trade and into our private lives.
The discussion considers "Classical liberal" but rejects it because it suggests looking backwards. "Finally, "liberal" may well be the perfect word in most of the world--the liberals in societies from China to Iran to South Africa to Argentina are supporters of human rights and free markets--but its meaning has clearly been corrupted by contemporary American liberals." Eventually, it accepts "libertarianism" or "market liberalism."
It combines economic freedom and respect for civil liberties, with "skepticism about the benefits of both the welfare state and foreign military adventures." The Cato approach is not pacifist, but also relatively isolationist outside trade relations. It rejects socialism and central planning, and takes a "cosmopolitan, inclusive vision for society. We reject the bashing of gays, China, rich people, and immigrants that contemporary liberals and conservatives seem to think addresses society's problems. We applaud the liberation of blacks and women from the statist restrictions that for so long kept them out of the economic mainstream. Our greatest challenge today is to extend the promise of political freedom and economic opportunity to those who are still denied it, in our own country and around the world. "