The Thames Barrier is something cool to see, too. It's on the DLR at Pontoon Dock station.
The British Museum is awesome, but it's easy to OD and get into info overload. There is sooo much there.
If you like theatre at all, there is a TKTS discount booth in Leicester Square that will have same-night tickets for almost anything playing in the West End, particularly on weeknights. Plus the Southbank Centre has some good concerts.
The "Dressed to Kill" exhibit at the Tower of London is good, if it's not super crowded and you're into history much. Kew Gardens was a nice relaxing afternoon, too.
Get a visitor's Oyster card before you go, and save yourself some hassle. In the US you can get them online from BritRail or VisitBritain. And if you're going to be there for two weeks, get on a train and head out to other places.
And I took my netbook, to save pictures off my camera and do some school work. The Starbucks in London (they're even more numerous than in NYC, I think) have wireless that isn't free, but is at least reasonable and you can buy minutes that can be used over multiple sessions.
I love London. While the Underground is super easy and goes all over the place, just walking is fascinating. There is such a mix of old and new architecture, and cool little things tucked all over the place.