I've had a love affair with the BT Tower for some time now. Unfortunately entrance to the public was shut in 1980, but earlier this year I was invited up to the top, where the revolving restaurant once stood. The views were absolutely breath taking.
Slightly biased as this is where I live, but Stoke Newington is great place to spend lazy saturday / sunday afternoons getting sloshed with friends. There are 10 + pubs within walking distance who all are great places for one reason or another. I'll pick out the White Hart for its huge beer garden...
London has plenty of beautiful cemeteries. Brompton is one of the ‘Magnificent Seven’ and has many interesting tombs. It was also an inspiration of names for Beatrix Potter and the resting place of Emmeline Pankhurst.