Hello EdgarCorrea
Yes, these trips will be covered by the Saver Day Pass. It grants free travel at will on trains, buses, trams, boats, etc. to inhabited places and cities. It rarely covers mountain trips, Mt. Rigi being one of the exceptions. You can find the map of validity for the Saver Day Pass here: Saver Day Pass – book earlier, benefit more. | SBB → Downloads
I strongly suggest buying the Swiss Half Fare Card in addition: Swiss Half Fare Card. | SBB
Furthermore, since you will stay in the Berner Oberland for a couple of days, the Berner Oberland Pass in combination with the Swiss Half Fare Card would mean a real bargain. The Berner Oberland Pass is on offer from April trough October, yet has a wide range of validity. And, with its Half Fare Card option, the Swiss Half Fare Card will pay off by itself. More info here: Berner Oberland Pass - Your travel ticket for the entire Bernese Oberland
If you are visiting Switzerland for the first time, you should Lucerne not give a miss. A night or two in Lucerne will be a great idea, it is the most visited city for a good reason, and truly Swiss.
You can travel from Interlaken Ost to Zurich HB via Lucerne. Interlaken to Lucerne is a very scenic ride: Luzern–Interlaken Express | MySwitzerland.com
If you need further assistance in planning your trips, for example if you have questions about excursions to particular places or if you want to have proofread your travel itinerary, there are two free travel forums voluntarily run by locals that can give excellent advice on that:
- TripAdvisor Switzerland (English language page)
- myswissalps.com
In the SBB Community, we are the experts on tickets, travel passes, and travel on public transportation services in general.
Please let us know should you have more queries.
Kind regards,
Roland