Murren is great, Zermatt is great, Chamonix is great - I love them all... and all have June Alpine weather - usually good - but 9 nights in the western Alps would be redundant (to me).
One can get to the eastern Dolomites directly from Marco Polo airport using the Cortina Express bus (about 2 hours) and local buses will take you from there across to val Gardena easily enough - Enjoy the scenery and leaving the driving to them! Kastelrotto is much smaller than the other val Gardena towns (Ortisei, St. Christina, Selva) and if your objective is the Alpe di Suisi one can get there from Ortisei as well as Kastelrotto.
Check out Gillian Price's hiking guides to the Dolomites. And since your hotel will give you a local bus pass you can go up one lift/gondola and come back down another and catch the local bus home.
https://www.suedtirol.info/en/en/
It is an hour by bus to Bolzano from val Gardena (stop for a mid-day visit to Otzi the Ice Man), and there are frequent trains across the Brenner Pass to Innsbruck. Innsbruck north to Luzern takes about 4 1/2 hours, through lovely countryside. OR, you could go south from Bolzano to Lugano (5 1/2 hours) on the Swiss-Italian border for a night (Swiss efficiency with Italian eating) and then take the Gotthard Pass route from Lugano under or over the mountains to Luzern. The Gotthard Pass Express route includes a lake steamer ride from Fluelen at the south end of the lake to Luzern.
One could spend LOTS of time in the Berner Overland, whether in Lauterbrunnen or Murren, etc. There is never enough time. But after that I might head to Murten (on the Swiss plain for a rich lowland experience) and then to Lausanne (there are great wineries on the north shore of the Lake of Geneva) even if you have little use for the Olympic museum. Zermatt deserves a stop but the hiking in June may be constrained by it still being winter-ish/wettish at higher elevations. The same can be said for Chamonix, but both are lovely mountain places. Both are also overbuilt but cater to the hiking crowd in the summer. Chamonix can be reached from Martigny near the east end of Lake Geneva, although the train connections seem weird since the train schedules from each side only route you to the French Swiss border town on the way
In my opinion Zurich sometimes gets a bad rap as being too "modern" but the Swiss National Museum there is a rare and excellent gem that might be worth a stop n the afternoon before your flight home since you are planning to be there that night anyway.
Have fun. Bring sturdy shoes, good base layers and a waterproof jacket.
