The most famous example is that of Kyoto, which was taken off of the both the conventional bombing list and the atomic bombing list by the Secretary of War, Henry Stimson, for its cultural value. It's a complex case — I have written on it some here — but it is the only Japanese city that got an explicit "pass" at the highest level, literally being on a "do not bomb" list (and not because it was being "preserved" for atomic bombing).

I'm hesitant in posting, as I don't know anything more about this than is in the source I'll give, but since this is directly relevant to the question and not something OP is likely to find on their own, I hope it'll be allowed:

Somewhen in a British campaign in Italy, Tom Clarke was to order the shelling of a town called Sansepulcro. He didn't, however, give the order to fire, because he remembered reading an essay by Aldous Huxley describing what Huxley called "the greatest picture in the world". This picture, a fresco by Pierro della Francesca depicting the risen Christ, was in Sansepulcro, and Clarke didn't want to destroy it. So Sansepulcro was saved for it's cultural value.

Here is an article by the BBC on it.