I stepped off a plane in Heathrow in Nov 02 with a free day and simply asked about lodging at a "information" booth in the airport. It's not the best way to go, but I ended up staying in a very new and upscale business taylored hotel south of the Tower Bridge. This area is not "touristy" but is close by bus or the "Underground" or "tube" to most tourist destinations. The Tower of London was a short walk across the Tower Bridge and I jumped a red bus that allowed me to get off at all the tourist locations. The Tower of London is a biggie for armor, early weapons, crown jewels, etc. A "must do" in my book. I also walked 'the Abbey' and Picadilly Circle. Didn't have much time so I spent much of it on the open top deck in the drizzle with my Carhart collar turned up to my Gus Stetson. Eventually, I was spotted by other American tourists and they joined me in the drizzle on top.