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.
The second coffee shop has to be Kaffeine. Having only recently come across this one, I was certainly impressed and they may even have the best coffee I've had, since a short stay in Portland, Oregon.
On a hot day there is nothing better to do in London then go for a swim in the Heath ponds. You get completely transported you out of the city as Hampstead feels like being in the countryside except you're in central London?!
A beautiful and spacious (outside of rush hour) way to get from Highbury, through east London to south of the river in minutes. The train snakes epically through Hoxton and Shoreditch and opens up the Jubilee Line via the beautiful Canada Water / Bermondsey stations.
It's a members-only library but you might be granted access with a research request. The writer's room is great but there's a few special, hidden corners among the bookshelves to tuck yourself away in.