Speaking of longitude, Greenwich also figures heavily in the history of navigation and timekeeping. The Royal Observatory was founded in 1675 with the mission of compiling a star atlas that could be used for celestial navigation by ships at sea (it took over 100 years to compile). Although latitude (north/south position from the equator) could be determined pretty easily from the Sun or the North Star, longitude was a much more difficult problem, requiring either multiple observations of the stars and Moon, coupled with a detailed almanac, or an accurate way of keeping time at sea, allowing navigators to compare their local noon (Sun at zenith) with the time at a reference location (Greenwich, which is zero longitude) and from that determine their east-west position.
The solution of this problem by carpenter-turned-master-clockmaker John Harrison is told in the wonderful little book Longitude by Dava Sobel, and if you visit the Royal Observatory, you can see the four amazing timepieces (called H1 through H4) that he designed and built over many years to solve this problem, overcome the interference of various rivals, and finally win the government prize of £20,000 that had been established for solving the longitude problem. Harrison was 80 when he finally got the money! I was shocked by how small H4 is - more or less an overgrown pocket watch (you can see pictures and read about the solution of the problem here).
There are many other instruments on display (including the 28 inch refractor shown above), and of course the chance to stand on the meridian line and thus be in both the eastern and western hemispheres simultaneously (a required photo op). There is also a newly revamped astronomy museum with interactive displays and a planetarium, the only part that isn't free (the show about how stars evolve and work was pretty good). I also visited the nearby National Maritime Museum and enjoyed the views of London from the high hill in Greewich Park on which the observatory is located.