Eric Rohmer in the rue de la Huchette c.1956
The location in Rohmer's La Sonate à Kreutzer that has excited the most attention since the film's recent rediscovery is the Cahiers du Cinéma offices, where we find André Bazin:
Claude Chabrol:
Charles Bitsch and François Truffaut:
As well as these cameo appearances we also find here, as actors in the drama, Jean-Claude Brialy, Jean-Luc Godard and Rohmer himself:
The film's principal location, however, is the apartment occupied by the protagonist (Rohmer): 
This is in a building at 96 avenue des Ternes, 17e, and overlooks the junction of the avenue des Ternes and the rue Belidor. The building was demolished in the 1970s. It was accessed via the villa des Ternes:
The film offers several views of the avenue des Ternes, in both directions:
The next important location is the rue de la Huchette, 5e, a street full of restaurants, bars and jazz clubs. We see two men (Rohmer and Godard) enter an establishment at no. 22. At the time there was a restaurant here called Le Petit Chevreau (it is now the Auberge du Moulin):
The exterior we see doesn't seem to match the supposed interior. The door Rohmer enters by (below left) doesn't look like the one Godard leaves by (below right): 
The interior shown is a bar decorated with distinctive murals:
I haven't been able to establish where this is filmed, if it is not 22 rue de la Huchette. It seems to be a vaguely Latin-themed bar, since writing on the door announces a South American soirée, 'Réveillon en Amérique du Sud':
The film also shows a typical Latin Quarter jazz cellar, with dancing to a trad ensemble:
The saxophonist in this group is Marc Laferrière, a very early appearance by one of the great exponents of New Orleans jazz, French style:
Laferrière is still performing with his Quintet to this day, almost sixty years later. (Visit his website, here, for full details of his career and upcoming concerts.)

Laferrière has identified the cave à jazz in Rohmer's film as Le Bidule, at 10 rue de la Huchette (now a Greek restaurant). Le Bidule was immediately opposite the much more famous Caveau de la Huchette, which still survives as a jazz venue (see here).
La Sonate à Kreutzer also documents the dancers at Le Bidule:
Rohmer includes a mise-en abyme of this effort to document by having Godard's character take photographs of the scene:
Real photographers were also interested in documenting the musicians and dancers of Le Bidule. Here are some photographs taken at around the same time by Paul Almasy:
The first of these photographs has sometimes been wrongly labelled as Le Tabou, a larger and more prestigious jazz cellar in Saint Germain des Prés. Similarly, this famous photograph by Willy Ronis is often identified as the Caveau de la Huchette, when it is clearly Le Bidule:
Marc Laferrière has identified the dancer in Ronis's photograph as Mimi, a star of the Caveau de la Huchette, who would come across the street to flaunt her talents before the lesser dancers of Le Bidule. Laferrière also recognised a young man sitting to the right, with a cigarette in his mouth, as himself.

Most of the other locations in La Sonate à Kreutzer are seen only briefly. On his way to the bar Rohmer turns from the place Saint Michel into the rue de la Huchette and, having left the bar, he and the woman he is courting (Françoise Martinelli) are on the rue Francisque Gay:
The couple are shown in front of two cinemas. The films playing are, on the left, Amato's Gli ultimi cinque minuti [aka Les Cinq dernières minutes, aka It Happens in Roma] (1955) and, on the right, Autant-Lara's Marguerite de la nuit (1955):
The cinemas are the Monte Carlo and the Gaumont Colisée, at 56 and 38 avenue des Champs Elysées.

The Champs Elysées appear later, in daytime, in a shot of Rohmer and Godard arriving at the Cahiers du Cinéma offices (at no. 146):
Rohmer and Martinelli also appear on the rue Soufflot and the pont des Arts:
Rohmer returns to both these locations for his first feature film, Le Signe du Lion (1959):
We also see the couple crossing the place du Théâtre français and at the door of her hotel, unidentified:
Also unidentified is a building under construction, visited by Rohmer (he plays an architect):
The last exterior scenes of the film are when the protagonist drives to Neuilly, parking his car on the rue du Pont and then walking towards the pont de Neuilly:
The pont de Neuilly is another location Rohmer returns to in Le Signe du Lion:
The last exterior sequence of La Sonate à Kreutzer shows several different views of the riverside at Neuilly, as the man tries to kill time:
Before returning home to kill his wife.
My deep thanks to Marc Laferrière for all his help, and to Jean Rousseau, creator of the Lieux de Jazz à Paris website.