Make sure to walk over to the Ile-St. Louis which is connected to the island where Notre Dame is by a footbridge. Less tourists, better place to grab a bite or ice cream (see Berthillon) and a cool neighborhood.
Paris is my favourite city in the world. In fact, it's kind of ridiculous just how obsessed with it I am. Obsessed enough to turn my room into a shrine. Obsessed enough to spend the last two years learning the French language. One day I'll move there. If only they could balance their budgets.