This gets nebulous very quickly. Most of the early experiments in radio were at colleges, and universities. In many of these cases students were involved and its not hard to exaggerate that into a college radio first. It's easier to be concrete with facts like: WDBM 88.9 was the first college station to go HD.
Rather than bicker, here is a list of some that claim the title with legitimacy:
WIIT 88.9 (cable)
At the Illinois Institute of Technology carrier Current WOUB-AM 550 went live from Ewing Hall on December 15 1942.
WRUC was originally known as 2ADD and signed on October 1, 1920. Two young men broadcast 27 minutes of music. In 1940 the station was given its new call letters WRUC which stood for Wireless Radio of Union College. In 1975 WRUC went FM operating at 10 watts. In 1983 the station moved to 100 watts and moved it's frequency from 90.9 to 89.7.
WOBC-AM went live in initially in 1948 as cable station on the third floor of Towers Hall. Jim Yost and Don Roose kept the station running in that era.
WKAR 870 AM
In 1924 Michigan State University founded this station. WKAR (East Lansing) is licensed after experimental operations dating back to 1917. At the very least it is Michigan's first educational radio station.
WFIU 103.7 FM
On January 5, 1922 professor Rolla Roy Ramsey conducted a demonstration of "wireless telephony" for a group of 75 students and faculty. In his early experiments, Ramsey successfully received signals from as far away as Denver, Wichita, Pittsburgh, and Oklahoma City. By 1950 Indiana University was running an FM outlet.
...and read this too. Personally I feel that WKAR is the first public station, and that WRUC is the first "college" station. Any other contenders?