I stay at the Eugenie in the 6th. Small rooms,but ideal location with a lot of people walking thru the streets, tourists and locals, all day and night.
If your budget will allow, go to La Tour D'Argent for lunch. For less than $200 a couple, you will get some of the best food and spectacular scenery overlooking Notre Dame. I'm cheap (ask my wife) but this is the best $200 meal you will ever have.