I suspect most people have a reasonable sense of her highlights, most notably creating the role of 'Marian the Librarian" in The Music Man, as well as 'Cunegonde' in Candide and 'Miss Balish' in She Loves Me. There's a lot more, like Plain and Fancy, and The Grass Harp, along with numerous revival productions on Broadway, like The King and I, and Show Boat, and national tours of Funny Girl and The Unsinkable Molly Brown,
And lots more. Lots. But rather than go into it all, here's the musical section of when she received the Kennedy Center Honor in 2011.
There's another video that includes the biographical section of the evening, and it's quite good. But the voice and picture is out of sync, and there are Japanese subtitles which get a bit distracting, as well. But if you want to see it, you can watch here. (It says the video runs 35 minutes, but it doesn't. It's 17 minutes, and gets repeated.)
But I couldn't leave it at that. How can you honor Barbara Cook and not have Barbara Cook? So, here is a rare . video of her on the Bell Telephone Hour in 1960, performing a medley of two songs from...The Music Man!
(By the way, when she sings the counter-point song of "Lida Rose/ Will I Ever Tell You" with a barbershop quartet, I recognize them as the Buffalo Bills. They were in the original stage production of The Music Man with her, and then re-created their role in the movie.)