Visiting architectural and cultural monuments in Europe doesn't get old. But the question is would you still be doing it as much if you actually lived in Europe?
Living in Switzerland which is in central Europe, bordered by France to the west, Germany to the north, Austria to the east (as well as the tiny country of Liechtenstein) and Italy to the south, I have the rare privilege to be able to travel to many different places and countries by car within only a couple of hours. The problem is that, although I _could_ do this, I usually don't, due to laziness, cost of travel, and lack of time.
While distances in the States are much vaster, your country still offers a kind of diversity that you might expect from Europe or other places in the world. That's at least my experience from travelling through the US. While most of you speak the same language, it's still very much different whether you go to Florida or to Minnesota. Architectural in Chicago differs from San Fransisco. Etc. Flights are generally much cheaper in the US, which somewhat makes up for the distances. Also hotels are cheaper - if you ever tried to book a decent hotel in Paris, you know what I mean.
For me personally, it's more about diversity than about how old a building is. That said, I could imagine myself just as much enjoying it in the US as in Europe; whether it's the Eiffel tower or the Empire State Building.
