Royal Observatory, Greenwich
The Royal Observatory was established in 1675 and has played a significant role in the history of astronomy and navigation.
The prime meridian passes through the observatory and has given the name GMT (Greenwich Mean Time) to the timezone, which lets you easily travel between the eastern and western hemispheres of the world. The area also has a planetarium built in 2007. The museum itself is located at a high point in Greenwich Park, which gives a great view of the city and especially of Canary Wharf.
You can get to Greenwich via train to the Greenwich station, about 15 minutes away, or the Thames Clipper, about 10 minutes away by foot. The DLR light railway also has a station at Greenwich and Cutty Sark.