Hi Mneo, I would recommend that you stay at MIJE. These are upscale Youth Hostels owned by the City of Paris.
These are in fact 3 different hostels in beautifully restored historical buildings located in the best possible area in Le Marais close to the river and the Islands of La Cité and Saint Louis. From there you can walk to so many places, Les Halles, the Louvre, the Left Bank and the Sorbonne, Notre-Dame, the Latin Quarter, and more. It has great underground and bus lines right around there.
I have spent over 25 years of my life in the Ile Saint Louis right across the river from there. I often stay in these hostels whenever I have to do business runs to Paris. I highly recommend the place to all A.netters travelling to Paris. Breakfast is included in the price. Private rooms are available on request.