For some peace and quiet, right next to Notre-Dame, try the Hotel Dieu. Although this is a working hospital you are allowed into the central courtyard which contains a peacful garden . Somewhere to chill out away from all the tourists. In the same area you can go into Palaise de Justice and wander around the vast corridors of this Gothic pile. If , like me, you are a fan of the Maigret novels you can imagine the famous inspector haunting this building. The same site also includes the famous Sainte-Chapelle church with its stunning stained glass windows.