ZRH-Neuschwanstein - Swiss alps:

It's easy to go by train from Zurich airport to Fuessen/Neuschwanstein, but it takes about 5 hrs and involves some train changes at small stations, A car ride might be a bit faster, but I would never drive after a overnight flight.
From there to Lucerne, you may backtrack up to St. Gallen and change there to the scenic Lucerne bound Voralpen Express.

For a more scenic itineary, you may go from Fuessen/Reutte either by train via Garmisch or by bus via Nassereith to Innsbruck, visit Innsbruck and then follow the Inn river upwards via Landeck - Scuol-Tarasp (scenic village with castle and mountain thermal spa) to St. Moritz/Pontresina.
There you can either board the Glacier Express directly to Zermatt (takes the whole day) or the Bernina Express to Tirano followed by a bus ride to Lugano. The next day, you could visit the 3 castles of Bellinzona and go on by train via Locarno/Lake Maggiore - Centovalli - Domodossola - Brig to Zermatt (- Grindelwald - Lucerne - ZRH).

Swiss Alps ...
 

Thank you @Neckervd and PalenQ for your reply, the information about the weather condition is very helpful.
Thank you for your expert advice and details for all the possible scenic routes for our itinerary, which sounds very interesting.

Based on your suggestions and our priority, I would like to make a proposed itinerary for your review and advice, any suggestions are welcome:

Because we take this trip to Switzerland as an opportunity to experience the Swiss Alps, we would like to concentrate most of time in the area, we could have chosen a different month for better chance, but we are limited to June. We would try to make itinerary balanced, mountain vs lake vs others such as castles.

We probably won't go to Germany as a side trip, since it is a little too far, we are considering adding Annecy as a side trip since it is not too far and very close to Chamonix, the weather there seems a little better for the Alps. For the Zermatt area, you mentioned there are more to see, are these Brig, Lugano or Bellizona? Can we stay in Zermatt for two days, one day for Matterhorn, if weather not cooperative, opt for these backup plans? I would give extra days also in Grindelward to take a chance for good weather, so put Grindelward towards the end of trip. I read other threads about the Murren- Schilthorn Cableway, I can not resist not to go there. The following are the tentative itinerary:
June 8 arriving Zurich, tour Zurich, afternoon to Luzern
June 9 Luzern old town, relax
June 10 Mt Rigi plus lake luzern
June 11 Brienz, lake brienz boat, steam railway to Briener Rothom
June 12 From Luzern to Montreuz Is there a scenic route?
June 13 Montreux chateau d Chillon
June 14 Montreuz to Annecy Is there a scenic route
June 15 Annecy day trip to Chamonix - for Aiguille du midi cableway
June 16 Annecy to Zermatt
June 17 Zermatt Matterhorn if weather allows
June 18 Zermatt to Grindelward Is there a scenic route
June 19 Grindelward
June 20 Grindleward
June 21 Grindelward
in Grindelward if weather permits to Schilthorn, Mennlichen cableways, etc and various short trails
June 22 Gridelward to Zurich
June 23

Thank you so much!

@ jane86: I would strongly encourage you to start a new thread. Many of us open the link to see a post from 2015 and immediately close out -- as I've done for several days now.

Your new itinerary is not more scenic and has not more days in the Alps than the first one (even much less than my second proposal in post 21).
But it's perfectly doable.
I suggest to put the itinerary in a somewhat logical order, however:

June 8th: arrival at ZRH, direct train to Lucerne, Lake Lucerne cruise
June 9th medieval city and museums of Lucerne
June 10th: Rigi, Pilatus, Stanserhorn or whatever you like
June 11th: Lucerne - Schuepfheim - Soerenberg - Brienzer Rothorn - Brienz - Aar Gorge - Bruenig - Lucerne
June 12th: Lucerne - Brienz (stop over, visit Ballenberg) - Lake Brienz boat - Interlaken - Grindelwald
June 13-15th: Grindelwald

June 16th: Grindelwald dp 8.19 - Interlaken - Zweisimmen - GOLDEN PASS PANORAMIC EXPRESS - Montreux ar 12.13, hotel check in, lunch, trolleybus or commuter train to Chillon castle, visit, dp 17.05 by historic paddle steamboat along the Lavaux vineyards up to Lausanne ar 18.33. Have dinner in the historic city center of Lausanne and go back to Montreux by train (4 trains every hr, 20 min journey).

June 17th: Train to Lausanne, Lausanne port dp 9.25 accross Lake Geneva to Evian (France) ar 10.00, dp by bus SNCF 10.50 to Annemasse ar 11.55, dp by train 12.33 - Annecy ar 13.29. Visit, sleeep at Annecy (or much easier, but less scenic: train to Geneva plus bus to Annecy).

June 18th: Annecy dp by train 7.32 - St.Gervais 8.56/9.05 - Chamonix ar 9.48. Hotel check in, then gondola ride to Aiguille du Midi - Pointe Hellbronner - Entreves (Italy) and back by bus (last departure actually 17.35, timetable may change until June) through the Mont Blanc tunnel to Chamonix.

June 19th: Chamonix dp 8.54 by MONT BLANC EXPRESS to Martigny ar 10.36. Luggage into the lockers. Visit of the Roman theatre and other Roman stuff, the car museum and the Fondation Gianadda. Proceed then to Zermatt, may be with stop overs at Sion or Brig (Stockalper castle open until 4pm).

June 20-22nd: Zermatt. dp by train 16.37 - Zurich airport ar 20.14, change at Visp

Swiss Alps and beyond
 

Thank you so much for your propose itinerary for us which looks great @ nerckervd, will review them more.
Thank you @kja for your suggestions, I started a new thread, however, it might be beneficial just to continue on the old thread, otherwise we will lose some information.
Whichever is fine for me.

June 12 From Luzern to Montreuz Is there a scenic route?>

Yes the Golden Pass Panoramic scenic train goes from Luxerne to Montreux direct and always thru thrilling scenery - especially between Lucerne and Interlaken wheni goes up and over the Bernina Pass and Spiez to Montreux, plying an Alpine valley much of the way. Nice Panoramic Observation cars - GoldenPass Panoramic: A feast for the eyes! - GoldenPass - can book seats even with a pass or no ticket I think.

jane86 has started a new thread :tu:
https://www.fodors.com/community/eur...e-the-1663420/