Although I can't imagine a first trip to London to be complete without visiting the Tower of London, I was actually slightly disappointed in my visit here. First of all, the Tower is fairly pricey to visit (on the order of $17-18). Secondly, unless you take one of the tours, it's difficult to understand exactly what you're seeing, but the tour (at least with our tour guide) seemed to drag on forever. We finally wandered away from the tour having gathered the basic information on the Tower. The highlight of visiting the Tower of London is obviously the crown jewels. While absolutely magnificent, it's a bit disappointing that this is the only location within the Tower grounds where cameras are forbidden.
After seeing the crown jewels, take the time to go through some of the other displays at the Tower. The White Tower contains a nice collection of armor and weapons that I found particularly interesting.
Don't forget to track down a raven or two (one of the icons that the Tower is known for) while you're here as well. They're not hard to find and they can't fly away since their wings have been clipped.
You can also wonder through a gate on the Tower grounds down to the Thames for a nice view point of Tower Bridge and of the surrounding London riverfront.