In Scotland, we were going to Holyrood Castle (her home while she's in Edinburgh) and were stopped at the door. We couldn't see it. The queen was in. She was holding an invitation-only tea to the local philanthropists, and we weren't invited. So, we hiked up Arthur's Seat to try to catch a glimpse. We saw lots of people, lots of tents set up in the royal lawns, but no queen.
In London, we went to the changing of the guards at Buckingham Palace. I kept my eyes open for drapes moving in the windows behind. At one point I saw the royal duster, wiping the windows. I got pictures of the balcony where she occasionally pops out to wave. Still, no queen.
So where did I see her?
We were leaving Westminster Abbey, walking down the sidewalk. Suddenly, I saw a flashing light, like a police light, but no siren. I glanced over and, behind one motorbike escourt, was the royal driver with a miniflag flying above the car. In the seat behind him was the queen, with her hair neatly put up and her hat on. About 10 feet from me.
I saw the queen. :)