After 3 years of working nearby I finally tracked down the well at Clerkenwell and popped along one lunchtime.
The experience itself was as rewarding as the London Stone. I got to stand on a busy street and peer through a large window at the covered hole in the ground that is the well. One or two people walking past gave me some very strange stares.
There is a fair bit of history to read next to the well, but unless you either have the key to the room beyond the window or very good eyesight, you may have a few problems reading it.
Worth visiting if you are in the immediate viscinity but I wouldn't bother making a day of it...
AKA the well at Clerkenwell.
14-16 Farringdon Lane EC1.
The well is now in a locked exhibition space and can be seen through some large plate glass windows. The key can be obtained for unlocking the space iirc from the local library.