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.
If you want a peaceful day out of the busy city, Highgate doesn't really feel like London. The cemetery is interesting and peaceful, there's a tour of the old half which is definitely worth the money. Karl Marx, among others are buried there.
The Royal Park offers great views of London and the city; As well as housing the Royal Observatory which includes a museum of astronomical and navigational tools, part of the National Maritime Museum.
Netil360 is a great roof terrace bar near London Fields in East London. It is situated on top of an ex-Hackney Council Building. We were one of the first design studios to move into the building while it was still being converted into a creative hub. It is great to see that this place is still vibrant. It definitely has one of the best all around views of East London. I took this picture (facing South) in the summer of 2018. It shows the gasworks near The Oval Space in the mid-ground and the Shard as part of the London skyline.