Having just gone through the visiting colleges/talking with visiting college reps gauntlet, Princeton's reputation, at least anecdotally, as the most conservative ivy is pretty well established. Here are just a few reasons off the top of my head.

1. The persistence of eating clubs -- five of them are "selective" and go through the "bicker" process to select members.
2. Relative late in going coed. Princeton had no sister school, and went co-ed in 1969.
3. Backlash from going coed. By 1972, "Concerned Alumni of Princeton" was founded by conservative alumni unhappy with coeducation and the general liberal shift of the university.
4. There are a decent number of prominent conservative political figures who are Princeton alumni-- Bill Frist, Sam Alito (who was a member of Concerned Alumni of Princeton) Donald Rumsfeld, James Baker, Josh Bolten, Richard Perle, Steve Forbes and George Will, to name a few
5. Robert P. George, the prominent conservative political philosopher, teaches at Princeton. George also is the director of the "James Madison Program" - which is a research group that churns out a lot of conservative political theory. George is also frequently published in the National Review and First Things, so among conservative political philosophers, he is relatively prominent.
6. The Peter Singer hiring controversy. When Singer was hired by Princeton, conservative businessman Steve Forbes threatened to stop giving Princeton money, and in general conservatives raised a stink. In fact, the Madison program was created in the wake of the Singer hiring.
7. Among Ivies, Princeton is relatively more focused on sports, which can have conservative connotations
8. It's the southernmost Ivy.

There are probably some more reasons, and none of these are really evidence that Princeton is a "conservative school" or anything, but the reputation appears to be well established.