Ah, now you're on a subject after my own heart!
I'm sad that the US Senate Library reading room in the Captial (btw, the Senate Library is not a part of the LOC, but a different entitity entirely) is not on the list. Sadly, it's now the senate leadership's private reading room, but it's a beautiful room with a fantastic round window that looks out from the capital towards the Washington Monument. It's the one thing I do miss about working for the gov't.
I love the picture of the cathedral library with the chained books!