Not the most exciting place inside, but a lovely rooftop area which not all that many people seem to know about, 2 mins walk from Old St station. If it's packed then The Red Lion is just up the road.
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)
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.