??Is there a way to print a map of your train itinerary?

If you go to the German Rail query page and enter Luzern to Salzburg, you will get several connections. Next to each one is a ">" symbol. Clicking on that gets you the details of the connection and, at the bottom of the detail, is an icon and the words "show map".

My recommendation would be to fly into Zürich open jaws, see Zürich, go to Luzern, then take one long train trip to Munich (you can get a €39 Europa-Spezial Schweiz fare for that) and see Salzburg as a side trip, fly out of Munich. Lower cost, less backtracking.

I like Lee's suggestion, with only one possible caveat. If you like the prospect of a scenic rail journey change the routing so that you enter Salzburg from Zurich. This will require doing some backtracking.

Fly into Zurich, to Lucerne, back to Zurich, to Salzburg, to Munich, fly out.

The leg from Zurich to Salzburg can then be the Maria Theresa scenic ride. That train is outfitted with some special 'observation cars' in 1st class with larger and more scenery friendly windows. A similar train, though I don't recall the name, runs along the Zurich-Innsbruck route.

Wow. Thanks. I just followed the advice to click the > button. I can't believe I missed that. So sorry, everyone.

Thanks for all of your help. Our trip is actually a lot more complicated than I mentioned. We're actually flying into Geneva (our particular flight was cheaper than flying into Zurich). We're going to visit Lausanne, Montreux (using Lausanne as a base) and then head to Interlakken (base station for a few days, visiting Jungfrau etc), then off to Lucerne. From here, in some undetermined order we're going to do Munich, Innsbruck, Salzburg). Then Cinque terre (way out of the way, I know. We're fine with that). Then Rome. Flying back open jaw from Rome.

Once again, thank you all for all of your help!