The best hotel deal in Paris is Grand Hotel Francais - it's in the 11th, so a less touristy and more neighbourhood oriented part of Paris. It'll take a metro ride to get to the more famous districts, but it's close to transit. Always gets very high reviews on tripadvisor. I stayed there a couple years ago, was very pleased.
http://www.tripadvisor.ca/Hotel_Revi...de_France.html
You can feel safe in most of central Paris - it's always so busy on the streets it's hard to not feel safe.
Also, eat at Entrecote - a Paris tradition. Best steak frites.
http://www.relaisentrecote.fr/