re: You have four days in Paris - what do you do?

As an add on to the many great suggestions, I would add taking a stroll through Pere Lachaise (sp) cemetery. Many many famous Parisians buried there as well as Jim Morrison.

I'm a history buff and that was a very cool couple of hours there and its also away from much of the crowds. Think of it as an outdoor Westminster Abbey (Poets Corner, etc.)