I'm sure we are all aware of the movie Monument Men and United State's interest in preserving important cultural artifacts of Europe. I know that movie is not the most historically accurate film and the US may not have been too concerned for Europe's Cultural Resources, but it at least had some basis in reality.
The broad question I have is whether or not the US had concern for the destruction of Cultural Resources of Japan during the Pacific Theater. More specifically, did the US have concern for Cultural Resources of specific Japanese cities when choosing a bomb site for the atomic bomb.
The closest you have to the Americans caring about cultural resources is the non-targeting of Kyoto, which was justified as it being a cultural center. I have written about Kyoto here. I am not sure it really counts quite the same as the European example — it was literally the insistence of one person (Secretary of War Stimson) that led to Kyoto not being targeted, not any large bureaucracy or process or anything systematic. In general, the US was not particularly concerned with the destruction of cultural artifacts in Japan from either the atomic bombing or firebombing campaigns, both of which were flagrantly indiscriminate in their nature, targeting entire cities without attention to damage limitation.