Lots of traditional charming country pubs around the area, but it can a bit hit and miss. A really friendly one with amazing food (and a unusually large veggie selection…) is the Beehive in Epping Green; close to the Great Wood. It's friendly enough you dare going there by yourself with the paper and are not at the mercy of local rubbernecks ("the rubberneck" = person who stares at strangers without any sign of guilt)
These giant spectral cylinders are great at different times of the day but my favourite time is around dusk when the buildings in the city start to light up. The Gherkin and the new Shard building are framed in the lowest ring then the shifting colours of the sky are almost split in the following ellipses.
Lovely space in Southbank. Interesting events and exhibitions. I really like the surroundings as well, especially during sunny days. Walk around and then have a rest drinking facing the river.
The walk along the South Bank from Westminster to Tower Bridge will take you past a plethora or interesting sights and cultural hotspots. There's always something interesting going on too.
A place that really grows on you, with each visit the Barbican reveals more of itself to you and your bond is tightened. The Barbican Kitchen is great for coffee or lunch, summer hangouts by the ponds, cinema in winter, the amazing Barbican Hall for live music, and don't miss the conservatory.