Don't go to the main tourist area of the wall, get a ride either on your own or with a hostel to one of the more rundown areas and hike for hours along the wall. Careful though, it gets rough!
This is the room dedicated to the Enlightenment at the British Museum and at the risk of sounding a bit dramatic, I find this room incredibly humbling. I can never spend less than a few hours here and I've been many times at this point. Whatever you do, don't miss it.
This is a vacation all by itself, one could spend months in here, Don't sit outside and lean on the glass pyramid, It is'nt allowed as we found out., even for a picture.