All mentioned areas are worth a look. I'd say, you should start in Andermatt. There you are in middle of it. To the east you'll go to Graubünden. To the west over the Furka to the Obergoms, where you might head to the Grimsel and enter the Aletsch area through that passage. Or you head down the Goms valley until Bettmerboden, where you'll take the cable car up to Bettmeralp. A very nice area is also Val d'Anniviers, you'll lodge in Grimentz or Zinal, and then you have some 4000m peaks very close. Or in the next valley in Arolla.
Other suggestion: you go around the Engadin valley, check out Diavolezza, Bernina, the neigbouring Vale di Poschiavo, Vale di Bregalio, Albulapass. I can recommend Lai di Lunghin above Maloja, but it is a steep way. In the Heutal you'll have a good chance that some mountain goats chase you around. Whereas in the Valais the Ehringer cows are already back in the stable.
The Glarner Alpen are sometimes spectacular, but a really special area is Glattalp. You go to Muotatal, continue direction Bissistal until Saliboden. There you take the cable car up to the Glattalpsee. You can walk either to Braunwald or return to Saliboden with either cable car or walk. There is a bus from Muotatal until Saliboden. And if you call the cable car and reserve a place, then you don't wait!
The idea with the Jura is nice, but you'll see everthing form very far and it really depends on the weather. There are some days which leave you speachless, but those are very few and you can't tell them to come on the snap.
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