I doubt the faculties of many public universities could be considered "conservative" (their livelihoods are DIRECTLY tied to more government spending and higher taxes), but there are certainly varying degrees. For example, though both are liberal, the University of Iowa is certainly a bit more liberal than the University of Illinois.
Indeed. The best bet would be Deep South universities, in which the white vote is so overwhelmingly GOP that even professors likely are influenced to some degree by conservative thought. Also, community colleges in ultra-conservative counties in the Great Plains may show a similar trend.