A philosopher elsewhere wrote seeking advice for an undergraduate student of hers interested in "conservative" political philosophy, but neither in the libertarian nor Thomist traditions. She explains:
My student is interested in exploring a kind of conservatism of which Burke is just one example – other examples might be John Kekes, maybe Roger Scruton, John Gray. His thinking is decidedly anti-liberal, but he is interested in constructive conservative thinking rather than mere anti-liberal critique. My student’s conservatism is not grounded in religion, so a Catholic-heavy institution might not be the best fit. Political science programs are not out of the question, but he’d be looking for programs where one can do serious political philosophy.
My sense is there isn't a lot of interest in Burke in philosophy departments with PhD programs, but correct me if I'm mistaken. Suggestions welcome; signed comments (full name) strongly preferred. And give some details/reasons, please, for the programs you recommend!