As I am an engineering geek, I felt that one of my must see stops on my London trip was to Greenwich to see the Royal Observatory. I think many people go just to take a photo of themselves on the Prime Meridian. That is a draw, even for me, and it clearly was popular based on how difficult it is to actually have a moment to take a photo on it without tens of other people in your photo frame. The observatory has some really good exhibits both about the history of the actual observatory and also timekeeping in general. It explains how it was first important for sailing and navigation. It is educational, and the displays of old timekeeping devices and navigation astronomy tools is fascinating. Also, the observatory is up on a hill and offers outstanding views of the area.
Royal Observatory
Octagon Room
One of the historic tools used for astronomy
View to the north
View to the northwest
Prime Meridian with longitudes for many cities displayed
Self portrait on the Prime Meridian