Hi Ncatanzaro -
Welcome to my Swiss Alps.
It's nice to have enough time to look around a bit, instead of flying through each destination.
You'll have some time to look around.
There is lots of useful information on the Getting Started page and links on the various pages:
There are two indispensable tools for trip planning- the SBB timetable for all modes of public transportation, and a map.
This map is good for travel. Open the menus and check out "Traffic" under "Points of Interests."
You can see immediately the relative locations of your cities of interest. Zoom in to zoom level 32 and the railroads appear prominently, so you can see how the routes run:
This page explains how to use the "Advanced" timetable, which is the SBB timetable:
Please read the information there.
With those two resources you can lay out an itinerary which is the most effective at getting to your desired cities. You can also visualize that some cities are well suited for day trips.
If you want learn a bit more about the various cities and regions, check here:
Some comments about your destinations. -
As you will note in this link:
the seasons make a difference. And, altltude is very important.
In late may, Spring will be in full swing at lower altitudes. In fact, that is why I am planning my next trip for that time of year.
At high altitudes, near the Jungfrau, for example, it will be the tail end of winter, with Spring just beginning, , and is a "low season." Too much snow left on the trails for hiking and snow slides, not enough good snow for skiing. So, few tourists, and many (but not all) hotels and restaurants are closed. In the Jungfrau region, cableways and special locations are just beginning to run in late May. The cograil line to Kleine Scheidegg and Jungfraujoch runs all year. In May, you can get up to Schilthorn.
Search for names in the search function, for example, Schilthorn.
The wonderful , easy, scenic walk at Männlichen (above 2000 meters) will not open till June 15th in most years; maybe later this year if the heavy snow pack lingers:
The floor of the Lauterbrunnen Valley is usually pretty much snow free in late May. 8oo meters, but not a lot of full sun, because of the high mountain walls.
The point of those comments is to alert you that altitude makes a real difference, especially at the time between seasons. .
Unfortunately, the map I linked does not give altitudes.
City pages in this forum do:
Look down that page on the left.
This extremely detailed map does, too. You probably won't need it, but some people just like maps. ;-) Overkill for non-hikers, but you can get the altitude for any location if you need it: Enter a city name, such as Gruyeres, in the search box:
map.geo.admin.ch/?topic=ech&lang=en&bgLa yer=ch.swisstopo.pixel karte-farbe&layers=ch.bav.ha ltestellen-oev,ch.swisstopo.swiss tlm3d-wanderwege&layers_visi bility=false,false&E=2 571878.38&N=1157956.80 &zoom=5
<<"is St Moritz a must?">>
That's a personal opinion. It was for me on my first trip to Switzerland, bu I've only gone back once or twice to take guests. I go back to Luzern ( local German spelling) frequently, and Wengen a lot. To each his own.
However, if you want to rice the Bernina Express and go on to Lugano, it makes sense. Some prefer Pontresina, because you are close by, butnotpaying for the name.
Spring is the best time to see the Rhine Falls. Snow melt adds a lot of water. Powerful, impressive, not very high. If, by any chance, you have seen Niagara Falls in the USA and Canada, you will be underwhelmed. In that part of Switzerland, with your stated aims, I'd go to Stein-am-Rhein or further east to Appenzell and St. Gall.
Wonderful Old Town,for walking, the Abbey Library is a Unesco World Heritage sight....
If you do go east, Zürich is a pretty good base. Not terribly scenic,but good museums and restaurants. Some parts of the Old Town, on both sides of the river, are nice to walk through.
If you don't go East, you should look for bases at at places like Montreux (Lausanne is a compromise between Montreux and Geneva. Most prefer Montreux. I like both.)
Luzern- just barely on your list - but I'd put it first. That is the usual recommendation on this forum for the first time visitor. Close to Zürich, scenic, beautiful lake, nice old town, easy train ride to Bern or Basel....
And, then, somewhere near - not in - Interlaken. Even though it is low season the mountain villages are much nicer. I like Wengen. Other choices are good, www.myswis salps.com/interlaken
South of the Alps, Lugano on the way to Milano. Or, my preference, Locarno. Check them all out on the map., to see the travel logic.
Those are some thoughts for you to explore.