Getting from Innsbruk to Switzerland

There is a direct train from Innsbruck to Zürich every 2 hours, the trip takes 3½ hours. From Zürich you can get connections to Luzern (+ 1 hour), Zermatt (+3¼ hours), or anywhere else in Switzerland. See www.sbb.ch for times.
But, yes, this is a slow route. You are going along the Alps, so it is not fast, but is scenic. There is no real alternative as Innsbruck does not have an airport, nor does Luzern or Zermatt.

That is a huge help to know, as every option I could find was taking upward of seven hours. Thank you!

Some people go to Switzerland primarily for the scenic train rides and the route from Innsbruck through the Tirol region is also scenic. Of course, we like the idea of spending quality time on a mountain, instead of just passing by. The Berner Oberland is an alternative to Zermatt, even Rick's favorite over Zermatt, and a bit closer to your other cities. Check train schedules to/from Lauterbrunnen, for instance. Any of these mountain destinations require connections, but they go quite smoothly in Switzerland.

If you are looking for a city I would skip Zurich and head to Lucerne. It is gorgeous!

Chris F: Innsbruck certainly does have an airport, however the only flights relatively close by are to Frankfurt and Vienna. Switzerland is not served from there due to the train service being so frequent--and less expensive.

But you can get to Innsbruck from many far away places--like the U.K. and even Moscow.