My advice, do not stay in Zürich or Bern, they are not in the Alps. Bern is worth a visit, Zürich is nice, but lots of places are better, skip it.
After landing in Zürich, go first to Luzern. This is only 1½ hours from Zürich airport by train - easy. Trips from Luzern on the lake and up mountains (2-3 nights).
Then on to Zermatt. Make sure you go via The Brünig pass and Interlaken, i.e. through the Alps. Again 2-3 nights.
The best part of the Berner Oberland is above Interlaken (Lauterbrunnen, Grindelwald, Mürren, Wengen etc.). If you can spare 2+ nights for one of these as well as Zermatt, do so. But you only have 8 days (7 nights), so it is not possible.
Finally 2 nights in Montreux or Lausanne. Do the other as a day trip from whichever one you stay in. Bern can also be done as a day trip here.
You can plan this all out on the Swiss Railways map: https://www.sbb.ch/content/dam/sbb/de/pdf/freizeit-ferien/ferien-kurztrips-schweiz/internationale-gaeste/sts-geltungsbereich.pdf
You don't say where you are exiting from (Zürich or Geneva airport, or by land).