I am not a religious believer, and I do feel a pretty strong sense of awe in those thousand-year old European cathedrals.
I've got a special fondness for Westminster Abbey. It has a lot of historical connections that mean a lot to me. And it has Scientists' Corner, which includes Newton, Darwin, and Hawking.
Oddly, I didn't feel nearly as much awe at Notre Dame, and I've heard others say the same. Some have suggested that it's because the place was really stripped during the French Revolution. That's got a strong whiff of superstition, so I don't know if I really buy it. Perhaps I'll feel differently next time, when I can admire the way it's been rebuilt.
When I'm in a cathedral like that, I imagine what it was like when somebody laid down the basic outline of it on the ground and said, "OK, here's where we dig the crypt, and build up from there. We're gonna have to build the walls X thick because in a hundred years they're going to be hauling up stones for an arch tens of meters up."
I don't share their faith, but I can certainly understand how strongly they felt it.
So yes, I think if you ever make it to Europe, you'll really like sitting in one of those very big, very old buildings. Some are more dramatic than others, but practically every large city has at least one really amazing old church. And even the smaller ones can be quite moving, even if you don't care about the religion at all.