I was of two minds when I was deciding whether or not to visit - it's the prime meridian, so I thought I ought to since I was already in Greenwich, but astronomy is really not my thing. I'm so glad I went!! It was very interesting to see the evolution of the observatory and how astronomers evolved the setting of the meridian line, and which ones carry through even to today. Also interesting to see their historic instruments and how the lodgings evolved with the family size and needs of the royal astronomers over time.
One watchout - if you are walking up to the observatory from the Queens House or Maritime museum - Google maps says that it's a relatively flat half mile walk. IT'S NOT RELATIVELY FLAT. I'm fairly fit and I was huffing and puffing on the steep walk up to the observatory. I think there is car access - that's definitely the better way to go unless you're up for a light workout.