Agree on that secret. Sadly so much of the western world is really fat and out of shape now that even taking a cable car up a mountain and hiking for a few hours is out of the question, with a hike up/down mountains or even hills is completely out of the question.
The best thing about travel in the US is the national parks, IMO. A trip through the west visiting Moab, Arches, Canyonland, Rocky Mountain, Yosemite, Joshua Tree, etc. is cheap and gorgeous. Experiences that can't really be substituted through the Internet just because of the physical expanses.
It is true that Europe doesn't have the high mountain ranges of the Rockies, but we do have a lot of variety, and a lot of mountains. I'm in Austria which (IIRC) is 70% covered by mountains. There are so many villages and towns to explore that my wife and I spend our vacation just going on short day trips or 2-3 nights to somewhere we've not been within driving distance.
Personally I think an old country church or a little chapel on a mountain that is really only used by the locals for the last 300 years is just as cool as St. Stephan's or Notre Dame. Of course that is easy for me to say having been privileged enough to visit each multiple times.
I love looking at houses in different country and imagining how it would be to live there. Walk through streets that have been the same for hundreds and hundreds of years.