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.
Archive collection of surgical instruments - anatomy and pathology - dental instruments - medicine and surgery (basically a lot of dead things in jars, really interesting to draw from).
The Greenwich Observatory with its green laser beam can transfigure any night sky. If you decide to cross the Thames via the foot tunnel, make sure you look out for the green ray. You can be on one side of the meridian in a minute, and cross to the other side on the next, without even realising it.