We will be traveling by train from Munich to Innsbruck one day and the next day traveling by train to Lucerne. We will stay in Lucerne for one day and then take the train from Lucerne to Interlaken, stay there two days and then travel by train to Bern for one day and finally to Zurich. On the two days we are in Interlaken we plan on taking some of the mountain trains. Would we be better off purchasing a 5 day Eurorail Pass and paying extra for the Mountain trains or would we be better off paying for the trains from Munich to Innsbruck to Lucerne and then using a Swiss Travel Pass? Also since we would be taking the Mountain trains during the two days in Innsbruck, would the Swiss Travel Pass cover the Mountain trains on the extra day in Interlaken?
Without doing the arithmetic, I would say you are better off doing Munich - Innsbruck, Innsbruck - Luzern as advance purchase discounted tickets.
Once in Switzerland, your two options are a Swiss Pass, or a Swiss Half price card and ½ price tickets.
For all Swiss cities (Luzern, Bern, Zürich), you get a free pass covering that city only once you check in to a hotel. This does not cover you getting to that city, or travelling outside the city.
Since you can buy a cheap ticket from Innsbruck to Luzern, you only need a pass for 4 days:
- Day 1 Innsbruck to Luzern, covered by a discounted ticket.
- § Day 2 Luzern to Interlaken
- § Day 3 In Interlaken (up mountains?)
- § Day 4 To Bern for one night.
- § Day 5 to Zürich, as above, hotel gets you a city pass,but that doesn't cover you getting to Zürich
- Day 6 to Zürich airport. Hotel pass covers you. Even otherwise, this is a short trip, cheaper to buy a ticket.
§ = 4 days for which you need a pass.
A Swiss Pass covers some mountain trains, but not most. It is all detailed on the Swiss Pass Validity map here: https://www.sbb.ch/content/dam/sbb/de/infotexte/uebersichtskarte-sts.pdf
BTW, I am assuming "one day" = 1 night stay. I night stops are not usually a good idea, you waste ½ day travelling.
Have you got things you wish to see in Zürich. If not, and your flight out is not very early, you could go direct from Bern to Zürich airport
Why not "stay" in an alpine village hotel instead of trekking back and forth to Interlaken (which is not in the alps).