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.
Maybe an obvious choice, but the Barbican is always good. My favourite space in there is the curve gallery, last time I went was for Cory Arcangel's 'Beat the Champ'. I love the architecture, although not many people do. I think it was voted 'London's ugliest building' in 2003.
Small restaurant on Highbury Corner that started off focusing on (basically) posh kebabs, but which is now producing some of London's most innovative dishes, focused around unconventional meats, cuts, and breads. Not often you can eat incredible food while listening to heavy rock and metal, but Lee Tiernan has nailed a winning formula.
Wood-fired, Neapolitan style sourdough pizza in South London: soft, airy, slightly chewy and very light thanks to the extra-long dough maturation. Family friendly small venue walking distance to the Horniman Museum.