Apr 25, 2018 - 7:38 PM
Hello, Roro. I agree with Lucas that the Swiss Travel Pass is the best one to use in Switzerland and base on age, kids travel for free. I have used Multi-country Eurail passes twice on longer trips (lesser or no discount on certain Swiss mountain transportation) especially mountain rides beyond Interlaken Ost.
STP has better coverage and discount values. I think it is cheaper to use point-to-point tickets from France to Switzerland and from Swiss border to Italy (provided your schedule is final). Local tourist train and Metro passes in both France and Italy are cheaper than Eurail. If you order the point-to-point tickets from respective companies in France and Italy way in advance you can get a better deal. Swiss Travel Passes price never change regardless of when you buy them.
If you are taking TGV trains from France, take a look if the train workers strike is over or still in negotiation as it may affect your May 28 travel. French Railways (SNCF) is the only line affected though. While in Switzerland, some higher mountain transportations are not free but discounted.
If you are buying the Swiss travel pass, you might want to include a trip to Mt Schilthorn from Murren as the pass includes free travel for this year, 2018. While in Lucerne, you can also avail of the free travel to Mt Rigi (Vitznau to Rigi Scheidegg cableway) and Mt Stanserhorn (funicular and cable way). Titlis and Jungfraujoch are both discounted with STP.
If you are going south to Italy, you may want to start your Swiss travel from Zurich or Basel. Your Swiss travel plan (based on the places you mentioned) can go in the southward direction for efficient use of travel time - Zurich (north), Lucerne (north/central), Interlaken(central) and Montreux(south) and then to Italy. You can use one central base or change accommodation as you go to the direction of Italy (south). I hope this helps as well. Have a safe travel. Take care.