Here is my current list of 8 colleges that are largely free of regulation because they don't accept federal funds. It's not definitive since there are so many colleges in the US, but it's the longest I've seen. All are explicitly conservative save Principia which is affiliated with Christian Science.
I've included only four-year institutions (sorry Deep Springs College) that offer a general course of study. Let me know of any others.
Hillsdale College (1844), Hillsdale, Michigan.
Grove City College (1876), Grove City, Pennsylvania.
Principia College (1932), Elsah, Illinois.
Pensacola Christian College (1974), Pensacola, Florida.
Christendom College (1977), Front Royal, Virginia.
Gutenberg College (1994), Eugene, Oregon.
New Saint Andrews College (1994), Moscow, Idaho.
Patrick Henry College (2000), Purcellville, Virginia.
