I love the architecture of the Barbican - it is so important to its historical context, at a time when London was being shaped for modernity after the war - they also aspired to make it a bold art centre. We need bold, always.
Great selection of books and magazine with a big focus on rare. out-of-print books Japanese photography. Can sends hours in this little shop. I'd try to avoid on Market day (Saturday) if you want to have a good look as it can get a bit busy for such a small space.
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)
Audiophile paradise. Boasting one of the coolest looking and beautifully crafted sound-systems I've ever seen. More listening bar than club, it has a low key vibe with a diverse roaster of talented DJ's spinning an eclectic mix of tunes and full albums.
I grew up in Brighton which is full of cheesy bars like this. If you can handle being surrounded by multiple screens playing Kylie at full volume, its pretty much the cheapest bar in central london. The cliental is so varied its great for people watching and completely un pretentious.