Bellinzona to Zurich

I think your best bet is to take one of the direct trains to Luzern and spend at least 2 nights there. More day trip opportunities from there, as well as a great Christmas market. Then to Zurich for 2 nights, which also has big Christmas markets, including one inside of the main train station. From Zurich it is an easy half day trip to the Rhein Falls and back.

I'll try to talk you out of Liechtenstein as there is really nothing there. It is an indistinct section of what is essentially Switzerland. The only reason to visit to to check a box and move on. But if you really want to go, take the 171 Postbus from Bellinzona to Chur, then train to Sargans, then the 11 Postbus, which passes through Balzers and Vaduz.

Schedules at https://www.sbb.ch/en/buying/pages/fahrplan/fahrplan.xhtml

I once spend a few days in Buchs, just across the Rhine from Liechtenstein. I was there for Hilti, a major Liechtenstein based company that is so big it no longer physically fits in the country. Hence a lot of it is in Buchs nowadays.

Anyway, the joke in Buchs is that Buchs is the most boring place in Switzerland, and that is only due to Liechtenstein not being in Switzerland. Otherwise that would be the most boring place in Switzerland. As they saying goes: The place is "so boring they take the sidewalks in at night".

Ah Hilti. Even here in the States, when you need to drill a hole through concrete, "Get me the Hilti!"