There will be different answers depending on whether you are looking for a college where a majority of the students self-identify as conservative, or a college where conservative views are “welcome.” The answer is to the former is a more limited set of colleges, some of which have been named by previous posters— but the answer to the latter is “almost every college in America,” particularly when you added the qualifier “nonviolent”! The very purpose of a college is to encourage the exploration of ideas, the development of viewpoints, and the ability to articulate and debate these views.
College students have been peacefully protesting since the sixties and seventies and are doing so still. I went to college 1987-1991, and I recall students lying down in the mailroom at my college to protest the deaths during the Gulf War. But there also was a conservative talk show on the college radio station in which a pro-life (anti-abortion rights) position was advocated, so both conservative and liberal views were articulated. At my husband’s college, his dorm (which also housed the administrative offices) was briefly taken over by students protesting Senator Moynihan’s honorary degree.
Trying out and articulating views, and sometimes being overly dramatic in this process, is part of being a young adult. In some other parts of the world, some young adults throw rocks and molotov cocktails and strap on suicide bombs. In the U.S., students hold up posters and sometimes chant. This is peaceful and safe. It is part of the college experience. If you don’t want to participate, just walk past the protesters and ignore them. If you want to join a vocally conservative group, you will be able to find such a group on most campuses. Just check out the list of student organizations on each college’s website, and you will find them. You can email the student president of a group that matches your views to ask what the experience of having those views at the college is like.
I would say that conservatives articulating an unpopular stance (like the pro-life example above) are well tolerated everywhere, even at the most liberal-leaning colleges. People may disagree with them, and may offer counter-arguments, but they won’t be cruel to the speakers or exclude them socially based on their views. It can become more emotional and personal (though still not violent!) when someone specifically speaks out against fellow students— for example, saying that black students or immigrants don’t belong on campus is likely to draw a strong response from fellow students defending their friends. But conservatism and racism/xenophobia are not synonymous, so do not conflate them in thinking about how fellow students will respond.
Don’t fall for the false narrative. Extremist outside agitators on the right, and some on the left as well, are at times using visits of super-extreme speakers to campuses to provoke conflicts. They are especially successful at public colleges, like the recent incidents at UVA and Berkeley, because public entities are required by law to welcome almost any speaker to use their grounds. Part of the goal of these groups probably is to provoke a protest to feed the myth of a “close-minded educated liberal elite” in order to inflame less-educated voters to accept these extremist groups as political allies. Don’t take this narrative of the rabid-liberal college student as gospel.
In reality, the very purpose of a college is to explore various viewpoints and the factual background support for each view. College students will challenge viewpoints with which they disagree, and encourage people to back up their views with evidence… but the image of a conservative student being shouted down or excluded socially is more the work of fear-mongers than the reality of a college campus. But test this hypothesis yourself. Look up conservative groups on college websites and contact the student presidents. Are they happy or unhappy at their college? Find out! I bet you will be reassured more often than not.