At the TV station I was working for at the time (CBS affiliate in a one-station market) we were very glad to have Letterman, and we were carrying the lackluster Crime Time After Prime Time. I remember the viewing party for the first night, which a local radio station actually sponsored.
Was that either WLFI in Lafayette IN, WBKB in Alpena MI, or WAGM in Presque Isle ME? I can only think of three (at the time) single-station markets that would have been CBS. There may be others. (Though it really doesn't count as a market, WYMT in Hazard KY probably did whatever WKYT in Lexington, its parent station, did.)