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 Design Museum is a museum in Kensington, next to Holland Park, which covers product, industrial, graphic, fashion and architectural design. There is also a nice cafe on the 1st floor with beautiful views of the park.