What accent do those upper class, sophisticated people like Fraiser and Mr. Fenny have?

American Theater Standard. It’s what you learn in drama school.

“Im rich, bitch”

Kathleen Turner is the perfect “real life” example.

I personally love Gena Rowlands’ voice: http://tinyurl.com/genarowlands

Around here we call it “Locust Valley Lockjaw.”

From Wikipedia:

Locust Valley lockjaw is the colloquial term for a stereotypical upper class American accent associated with elite residents of the New York metropolitan area, particularly those on the North Shore of Long Island. The accent takes its name from the hamlet of Locust Valley, whose exclusive country clubs have included speakers of the accent. The accent is typically non-rhotic and involves speaking while keeping the lips tight and jaw clenched and thrust forward.

Individuals who have been described as affecting a recognizable Lockjaw accent include U.S. President Franklin D. Roosevelt, actress Katharine Hepburn, conservative commentator William F. Buckley Jr., Jane Hathaway, the secretarial character on The Beverly Hillbillies and Thurston Howell III, the millionaire character on…Gilligan’s Island.”