During the TMB you will pass by many refuges, some stopping for a coffee or lunch, and some staying for the night.
The following list of Refuges are where I stayed the night during my TMB in August of 2017. I have included links to the webpages and to their trip advisor page. See the individual posts for each day of the trip for photos and my experiences.
Day 0: Domency
Air BnB, there are many options in this area of the Chamonix Valley
Day 1: Refuge Nant Borrant
Day 2: Auberge de La Nova (Les Chapieux)
Day 3: Rifugio Elisabetta
TMB Website (English) (from TMB main page, their website is in Italian)
Day 4: Hotel Triolet (Courmayeur)
Day 5: Rifugio Bonatti
Day 6: Gîte de la Léchère
TMB Website (English)
Day 7: Pension en Plein Air (Champex)
Day 8: Auberge du Mont Blanc (Trient)
Day 9: Refuge la Boerne (Tré la Champs)
Day 10: Hotel le Morgane (Chamonix)