What area is safest to stay in Paris?

I am going to Paris on my own and I am going to stay there for a week. This will be the first time that I go there. So, I would like to ask you to recommend some area that is safest to stay in Paris and also that it is near to some major sights. I would really appreciate your suggestions and help.

We were in Paris three weeks ago and we stayed in Ile St Louis. The island is great and what more it is central to everything. It is two minutes from Seine. You cross the footbridge over the Seine and get to the metro. It is 5 minutes away from Notre Dame. There are so many great restaurants and shops there. Another safe place to stay is Ile de Paris. It is surrounded by St Michel, Chatelet and the Bastille. It is surrounded by tourist central and here you may experience the real Parisian atmosphere. You will be satisfied with whichever you choose between these two. Paris is one of my favorite Europeans cities.