We hiked the Tour du Mont Blanc last summer and absolutely loved the experience. I hope you do too.
You will,probably get lots of suggestions to stop in the Berner Oberland area around Lauterbrunnen Valley, but I have some different ideas.
The train from Chamonix Mont Blanc into Switzerland climbs to the border at Vallor one ( where you change trains across the platform) and winds along a ridge with great views to the valley below. You end at Martigney, where you meet the main east-West line connecting the Valais region with Lac Leman (Lake Geneva). The fast way to Munich would be to take the train from Martigney to Visa, where you change to a train through the deep Lôtschberg Basistunnel to reach Zurich.
I suggest you stay on that train past Visp to Brig. There you pick up a regional train continuing east upmthe Rhone Valley about 15 minutes to Betten, the valley station for a cable car that takes you up about 3500 feet to the carefree village of Bettmeralp. Spend two nights there to have time to explore the trails with views over the huge Aletschgletscher.
Then ride the cablecar back down, return to Brig, and ride the train north about an hour to the village of Kandersteg. Walk through the village to the gondola and ride up to the lake, Oeschinensee. You can book a room in the mountain inn there for a very peaceful night in a highly scenic area..
From Kandersteg, you continue toward Zurich, with an overnight stop somewhere fairly close to Zurich, but not in that city. Maybe Bern? From Zurich you take a direct train to Munich, in 4.5 hours. Or you could continue past Zurich and spend the last night somewhere on or near Lake Constance, and complete the shorter journey to Munich the next day.
I have left out Lichtenstein as it is out of the way and not really worth the effort just to tick off another country.