The Oyez Project, run out of the Chicago-Kent Law School, is a terrific resource for Supreme Court scholars. They have put online the audio of every oral argument going back to 1955, when the Court starting taping its arguments. I’ve been listening to some old ones (mostly out of curiosity), and one that is weirdly compelling is Time, Inc. v. Hill, a 1967 false light case that is still used in casebooks.
Hill was Richard Nixon’s only oral argument before the Court, and he ended up losing (5-4). I say “weirdly compelling” because it’s just fun to hear Nixon talking like an appellate advocate, going back-and-forth with Hugo Black, and so on. Check it out if you can. Nixon starts at around the 51:00 minute mark (arguments were longer back then).