Our first week was spent in London. Being tired, we pretty much wasted our first full day—all I wanted to do was sleep. (Having hit the pubs the night before had nothing to do with it. President's Courage bitters, I believe.) After we finally roused (about 2 pm), we walked. And walked. St. Pauls. The Thames. The Millenium Footbridge. The South Bank. The Tower. And we walked. And then we took the Tube.
I had never been to the South Bank, so that was a "priority" for me. Even though the Millenium Footbridge was still closed for "study," we visited a ton of sights on the South Bank, including the Eye (we were disappointed that every time we went to buy tickets, it was sold out at least 4 days in advance, so we didn't get to ride it), the New Globe, a replica of the Golden Hinde, the Imperial War Museum (I really liked the V-1s and V-2s, plus the re-creation of a World War 1 trench), the Tate Modern, the National Film Centre, the Royal Theatre, and the odd-ball things like the hot-dog sales people!
After a walk down Oxford Street and an afternoon stroll through Hyde Park (the original, I guess—lots of birds, including a Great Tit), we ended up at the Albert Memorial and Albert Hall. We also hit the Victoria and Albert Museum, while in the area. We walked back to Bloomsbury, but with a stop-off in Harrods and a stroll past Buckingham.
In the first week, we also hit the fascinating Cabinet War Museum, where Churchill conducted World War II.