There are so many cool things to check out in London it's hard to narrow it down. I'd spend a couple days just checking out all the traditional tourist spots and then just kind of get lost and wander around. We stayed in a holiday in right by heathrow because it was so much cheaper, but because public transportation is so good, it's really easy to get in and out of the city. Get yourself an oyster card which will cover buses and the underground.
We also rented a car and drove out to Stonehenge, which was cool to see.
Also drove down to Dover (like your name lulz), and stopped in Canterbury on the way down. It's a nice little town where you can go check out the cathedral, which is awesome...tons of history. In Dover there's Dover Castle, which is also very cool to check out.
I remember the name of one of the pubs we went to, Golden Fleece in City of London. It's kind of in between Millennium Bridge and Tower Bridge, by the MI6 building. I wouldn't go out of your way to go there, but it was pretty cool.