First of all, I recommend that...
First of all, I recommend that you stay on the left bank. The right bank is bigger, grander, and more expensive, but it is not nearly as homey, or exciting, as the Left Bank.
If you are traveling with a group, and are willing to spend about 30 dollars a night, I recommend the Hotel de Suez. This hotel has a great location; it is located halfway between the Cluny Museum and the Sorbonne on Boulevard San Michel(the main Latin Quarter boulevard). The staff is very helpful, and the rooms are adequate and clean. But the location is astounding for the price (about 60 bucks a night for two people). From the hotel, Notre Dame and St. Chappelle are a ten minute walk, the Cluny and Sorbonne are less than five, the heart of St. Germaine is ten minutes away, as is the Luxembourg Gardens. Shakespeare and Co. (the old English language bookstore) is also about ten minutes away. So, this is an all around great deal.
For a single traveler on a budget, I recommend trying to book yourself into the Association de Etudiants Protestant de Paris on Rue de Vaugirard in Saint Germaine. The dorm rooms are very basic, consisting of a bunch of sheetless and old beds lined up along a wall, but the rooms have large ceiling to floor windows that are always open in the summer. Once again, the location is the reason that I recommend this hostel. It is located across from a side entrance to the beautiful Luxembourg Gardens and is within a five or ten minute walk of the heart of the Latin Quarter and St. Germain. There is no lock out, but nothing is provided except the bed and a shower (you have to bring soap and a towel) You should get there at 8:45 in the morning to get a bed, because they do not take reservations, and you can stay there for five weeks, if you so choose.
Hotel de Suez runs about 30 dollars a person.
AAEP runs about 15 dollars a person plus key deposit.