Hut to hut walking is typical in Germany and Austria (and in some parts of Italy). Many huts there are like small hotels, with twin bed rooms, restaurants, etc. and can even be reached by car or cableway.
The huts of the Swiss Alpine Club are usually more spartanic, primarily used for ascensions of mountain peaks. Therefore, they are seldom situated along long distance hiking trails.
There are some exceptions from this rule, though. The following (spartanic) huts are on hiking trails: Cabane de Chanrion, Cabane de Prafleuri, Cabane des Dix, Cabane Bella Tola, Wildstrubelhuette, Cabane des Violettes, Bluemlisalphuette,Gspaltenhornhuette, Europahutte, Allmagellerhuette, Binntalhuette, Capanna Corno, Capanna Basodino, Capanna Cristallina, Capanna Cadlimo, Capanna Comarina, Capanna Scaletta, Capanna Motterascio, Capanna Terri, Capanna Tamaro, Chamona Kesch, Chamona Grialetsch, Rifugio Saoseo, Chamona Lischana, Camona Tuoi, Silvrettahuette, Seetalhuette, Carschinahuette, Schesaplanahuette, Enderlinhuette, Pizolhuette, Camona da Segnas, Camona Vorab, Muttseehuette, Claridenhuette, Glattalphuette.
There geograhical position is so different however, that a hut to hut hike between them is almost impossibble.
Swiss long distance hiking trails go often from isolated mountain hotel to isolated mountain hotel or to small villages with one or more small hotels:
Example: Verbier – Gde Dixence isolated mountain hotel - Prafleury hut – Dix hut – Arolla (mountain hotels) – La Sage (mountain hotel) – Zinal (mountain hotels) – (isolated) Hotel Weisshorn – Meiden (isolated mountain hotel) - Toerbel (small hotel) – Gspon (small mountain hotel) – Simplon Pass (3 hotels and nothing else) – Heiligkreuz (small hotel) – Binn (mountain hotel) – Binntal hut – Margaroli hut (Italy) – Zum Steg (small hotels) – Bosco/Gurin (small mountain hotel) ……..
If you look for a not too touristy Alpine Valley with good hiking possibilities and some bus and cableway lines in order to facilitate the hikes, check:
Val d'Anniviers: St-Luc, Chandolin, Zinal
Val d'Herens: Les Hauderes, Evolene
Val du Trient: Les Marecottes
Saastal: Saas Grund
In these valleys, you can take a bus resp cableway up to about 2000m of altitude, walk all the day at more or less the same altitude and use another bus or cable car line in order to go down in the evening.
Crossing the mountains on well signmarked trails and go down into the next valley is possible too. All valleys have excellent bus connections with the next railway line.
Another good choice may be the Engiadina Bassa (Scuol-Tarasp and surroundings), although there will be more people than in the above mentioned valleys of the Canton of Valais/Wallis.
Ryanair flies from Stansted to Turin, a good strting point for hikes in the Aosta Valley (hut to hut possible; overcrowded in August)
Eaasyjet flies from London to Geneva, Basel, Zurich, Lyon, Milan and Salzburg