Photo courtesy flappingwings

I leave Sunday night for a 9 day trip to Scotland with my father. The travel around Scotland will be planned as we go along by my father and I. At this point, the priority of things I want to see consist of 1) family roots and places my father went to school while there as a child, 2) Scottish history, specifically some William Wallace stuff as well as the highlands, and 3) anything else we decide to go see.
I fly into London, where I’ll have about 24 hours to see the sights before hopping on the train to Scotland where I will hook up with my dad. So this week’s question (nothing like waiting until the last minute):
What are some things I should be sure to see while in London?
Bear in mind, this is my first time to Europe so I will want to see some of the mainstays. St. Paul’s Cathedral, Parliament, etc. What else should I try to take in along the way?
Please give me your recommendations or experiences in the comments below. Thanks a lot. I will try and update you as to what I see after my 24 hour London plunge is complete. Updates will be in the comments as well.