Overwhelmed by itinerary options

I get some comments about always answering every question with “go to Budapest” and yes I overdo it at times. But your enjoyment of wandering the streets from morning till evening is pretty much what Budapest excels at providing the environment for. Tired? The new and old trams are amazing substitutes for HOHO busses. They go to all of the places you would want to see, they are cheap, and they are sort of fun.

Because Budapest isnt about a “tourist district” you can get lost and avoid tourists for hours without getting bored.

Some things going on while you are in the area:

Jewish Summer Festival Date: Aug 30, 2016 - Sep 6, 2016 (very excellent)
Foie Gras Festival Date: Sep 4, 2016 - Sep 6, 2016 (going this year for the first time myself)
Budapest Wine Festival Date: Sep 7, 2016 - Sep 11, 2016 (very excellent)

At the opera: La Traviata

At the operetta: Sybill buy tickets

At the Operetta Theatre: Sybill, The Gypsy, Forest & Romeo and Juliet
At the Liszt Academy: Not published yet, but always has very excellent classical performances
At the Opus Jazz Club & Budapest Jazz Club: Not published yet, but they attract some of the best jazz musicians in the region

Rick's Austria travel priorities put Innsbruck lower on the list than your other destinations. (Back when he had Germany and Austria combined in one book, he didn't cover Innsbruck at all.)

Other, cross-border cities can be reached with similar timing to Innsbruck:

Salzburg-Innnsbruck 2 h
Salzburg-Munich 1.5-2 h
Vienna-Budapest 2.5 h
Vienna-Bratislava 1 h

You don't need a lot of language skills for train or bus. Just buy a ticket to your destination. The smaller towns are also used to tourist. If buying from a staffed window, you can write down the key facts - destination city, time, etc. See also https://www.ricksteves.com/travel-tips/transportation/trains/buying-tickets.

Vienna is a given,so much to see with all of the Habsburg History.I have stayed in St Wolfgang on the lake front and it is such a relaxing atmosphere,great place to stay,there is the cog rail to the top of the mountain with great views of the lakes and valleys,you can ride the boat on Lake Wolfgang and get off at St Gilgen and also Strobl.In Obertrun there is the five fingers overlook with hike from the tram and the ice cave tour on the same gondola at a different exit.The salt mine tour in Hallstat is worth doing as well as visiting Hallstat as a day trip.The Melk Abbey is a must see with its view of the town and river.
Mike

With such a short time frame, you'll be limited in how many destinations you can fit in. There are lots of possibilities and this is one suggestion.....

• Vienna (5 nights) - tour sights in the city as well as a few day trips. As I recall, there are organized one-day tours of the Wachau Valley, etc. from Vienna so that would allow you to at least see it. Budapest is about 2.5 hours each way from Vienna, so a day trip would be possible (albeit a long day).
• Hallstatt (2 nights) - By the time you finish touring in Vienna (and with the jet lag), you'll probably be ready for some R&R, and two nights in Hallstatt would be perfect. I wouldn't suggest one night as that doesn't really allow any time to see much. The Salt Mine is worth a visit (IMO).
• Salzburg (5 nights) - again, do some sightseeing there as well as some day trips. One very picturesque small town is Berchtesgaden, which is in south eastern Germany (somewhat of a notorious history, if you're interested in that). You should be able to see some Mozart concerts in Salzburg (although I haven't checked).

I like Ken's idea! Hallstatt definitely deserves more than just a pop in / pop out day trip. And, as seasoned travelers, you know that when it comes to changing "home bases" it always takes longer to get from Point A to settled in at Point B than anticipated. Just stick with the 3 places & times Ken mentioned and avoid using good "seeing / doing" time changing locations.

Innsbruck is good for its location - access to the mountains. But I did not think there was much of interest in the town itself to merit three days. Just my opinion after one visit.

Language issues no worse than anywhere else.

Thanks to each of you for your ideas! It's definitely helping us firm up our plans. We'll lock in Vienna hotels and find hotels in Innsbruck & Salzburg which we can no-cost cancel. Then once we get there we can modify our plans for most flexibility. We'll also eat the extra cost of buying train tix at the station rather than locking in now.