The Lincoln Memorial in Washington DC is probably the first place I remember feeling a sense of awe. I was 5 the first time I visited the Lincoln Memorial, and the signs instructing guests to be quiet, the lighting in the hall, and the heavy feeling of history hung closely about, making me feel an awe of something I couldn't quite put a finger on.
I've been back to the Lincoln Memorial a number of times since then. It's generally held for me that same sense of quiet mystery. It is a melancholy place for me, for reasons that I can't quite explain. Perhaps my favorite visit to the Lincoln Memorial was when I went alone one afternoon a few years ago. It was a cold winter afternoon, with bright sunny weather. It was a perfect spot just to sit and think, and to soak up the quiet.
It's especially lovely to sit on the steps of the memorial in early evening, looking across the manmade pond to the Washington Monument. The serenity of that spot, right in the middle of downtown, is hard to beat.