The Left Bank near Paris-Sorbonne University and the Musée de Cluny is full of small, quaint and generally reasonable hotels. This neighborhood is an easy walk from Notre-Dame de Paris. We happen to like the Hotel du College de France, but there are many like it. Breakfast is likely to cost extra but be WELL worth it. Be prepared for tiny, tiny rooms -- they're the norm. Try to think of this as intimacy.

The Hotel Eiffel Turenne is just a walk away from the Eiffel Towerand even closer to Cler St a great market street to get some picnic items (and its my favorite thing about Paris). I recommend booking the hotel early... It can get booked quickly and they have a limited amount of rooms. Its a great place to stay if you don't mind small hotel rooms! 

Well the last 2 trips we have made both with 2 teenagers and then just the 2 of us, we stayed at a small hotel on Monsiuer Le Prince in the Saint-Germain-des-Prés walking distance from a Monoprix and the Odéon Metro station and best right above the Polidorrestaurant that Ernest Hemingway wrote at and the movie Midnight in Paris filmed, all at being said there is no lift..not uncommon in Paris..and very dated but it's very inexpensive €70/night for single and €110 family at Hotel Stella. Cash only, reservations by email. It's all about the location! Oh, and it's around the corner from Luxembourg Garden a Paris Bld Saint Germain and a lovely patisserie! 

My favorite hotel is the Hôtel Chopin. It's not quite in the middle of the city but it's very, very conveniently located near metro stops and easily within walking distance of some great areas. In the off season, they often have rooms for 58 euro a night. It's certainly not glamorous, but it's very reliable and clean and looks just like what you would think a small Parisian hotel would look like. 

Try the Hotel Saint-Louis en L'Isle; Right Bank, Fourth Arr.  It's a wonderful location; rooms are rather small, but not unlike most similarly priced hotels in Paris.  Others:  Hotel Saint Jacques, Panthéon, Hotel Des Grandes Ecoles.  Budget hotels: Hôtel Jeanne d'Arc, Hôtel Diana, Hôtel Eugenie, Hôtel Saint-Pierre and Hotel du College de France.  Travel and Leisure did an article on Affordable Small Hotels in Paris, April 2012 and The Guardian has good advice as well: http://www.guardian.co.uk/travel/2011/may/06/top-10-budget-hotels-paris

Hôtel La Louisiane is located in the heart of St Germaine des Pres in the 6th on the left bank.  I first stayed here in 1986, having discovered it by shear luck; and I once stayed here in 2003 and discovered a famous American film director staying here as well (don't want to give away his secret lodgings).  As for location in central Paris, it doesn't get any better. The hotel is comfortable but not luxury by any means, more location and access to all Paris has to offer just outside your hotel entrance.

Hotel Sofitel Paris Le Faubourg is very reasonable...though not really centrally located.