Anyone, American or not, who has an opportunity to travel to Washington DC should, if at all possible, visit the Lincoln Memorial. It is my favorite secular building because it is the one place that has such a grace of history, dignity and inspiration that no one can fail to be uplifted and heartened by a visit.
http://www.nps.gov/linc/
It's been many years since I paid my visit as an adolescent with my brother and sister in law while we were tourists to Washington DC. (By the way, that was also the occasion of my first visit to a mosque).
The Lincoln Memorial captures and magnifies in its very structure and design much of the spirit of Abraham Lincoln, his burden and his triumphs, in a way that no one can fail to derive much inspiration from, and an instinctive sense of who he was and what he did. The memory of such a visit, taken with such an attitude, will never fail the visitor, even years later. I love to think about my visit and I wish I had my photographs from that time with me so I could check them out again, me (young and slim!) next to the statue of Lincoln.