She was in the American Shakespeare Festival that performed Troilus and Cressida at the White House during the Kennedy administration.

She received a Primetime Emmy Award nomination in 1980 for her portrayal of Tallulah Bankhead in the television film The Scarlett O'Hara War.

That same year she returned to Broadway to perform the role of Lorraine Sheldon in a revival of The Man Who Came to Dinner.

In 1984, Nye was cast on the daytime soap opera Guiding Light as Susan Piper, an unscrupulous real estate agent going to great lengths, including murder, trying to reclaim a cottage that harbors a deep secret.

Her portrayal of the villainous character proved popular for some time, culminating in a location shoot in Barbados, ending with a memorable death scene where she fell into quicksand.

Nye and Cavett bought Tick Hall, a house in Montauk, New York, designed by Stanford White.