The New World doesn't have the age of churches and cathedrals you're discussing, but it does have some beautiful structures. One U.S. architect, in particular, has a style that he has adapted for various locations to pull the out-of-doors into the building.

Fay Jones was from Arkansas and has built chapels around the US.

In New York City there are churches built at the time of U.S. founding fathers but one that I always enjoy visiting is small in scale but important in American history, mostly because of who is buried in the churchyard. Trinity Church has been on the site, in three different versions, since 1697. The current (third) church was completed in 1846.

This atheist is perfectly happy enjoying the history, art, and architecture of these structures.