It is a tad bit embarrassing for me that I lived in New York for almost three years and never went to the Morgan Library. I remedied that this past weekend, and it was absolutely wonderful – I highly, highly recommend it to all book people.
It is a good size for a library-museum; you can see pretty much everything in under two hours without rushing. (Everything on display, anyway; there are treasure troves in underground vaults.) One room had a small Shakespeare exhibit, with early portraits of Shakespeare and a First Folio(!). The Diary exhibit upstairs was also wonderful; it featured quite a range of famous literary people, and showcased their tiny handwriting, inscrutable shorthand, and beautiful sketches.
Most of all, though, the library itself was stunning. On display was one of three(!) of the Gutenberg Bibles in the collection; music manuscripts from Mozart and other composers; beautiful illuminated manuscripts with jeweled covers; and early editions of every major work of fiction you could think of: Chaucer, Dickens, the Brontes, Shakespeare, Jonson. These were locked away, not on display, but the spines are visible behind glass.
As far as I know, Morgan did not spread the literary wealth the way that Carnegie did, but if you do have a chance to visit the Morgan Library, go!